Tootfinder

Near-optimal convergence of the full orthogonalization method
Tyler Chen, G\'erard Meurant
https://arxiv.org/abs/2403.07259 https://

Near-optimal convergence of the full orthogonalization method
We establish a near-optimality guarantee for the full orthogonalization method (FOM), showing that the overall convergence of FOM is nearly as good as GMRES. In particular, we prove that at every iteration $k$, there exists an iteration $j\leq k$ for which the FOM residual norm at iteration $j$ is no more than $\sqrt{k+1}$ times larger than the GMRES residual norm at iteration $k$. This bound is sharp, and it has implications for algorithms for approximating the action of a matrix function on a…

This https://arxiv.org/abs/2208.13190 has been replaced.
link: https://scholar.google.com/scholar?q=a

Exploiting higher-order derivatives in convex optimization methods
Exploiting higher-order derivatives in convex optimization is known at least since 1970's. In each iteration higher-order (also called tensor) methods minimize a regularized Taylor expansion of the objective function, which leads to faster convergence rates if the corresponding higher-order derivative is Lipschitz-continuous. Recently a series of lower iteration complexity bounds for such methods were proved, and a gap between upper an lower complexity bounds was revealed. Moreover, it was show…

IOI: Invisible One-Iteration Adversarial Attack on No-Reference Image- and Video-Quality Metrics
Ekaterina Shumitskaya, Anastasia Antsiferova, Dmitriy Vatolin
https://arxiv.org/abs/2403.05955

IOI: Invisible One-Iteration Adversarial Attack on No-Reference Image- and Video-Quality Metrics
No-reference image- and video-quality metrics are widely used in video processing benchmarks. The robustness of learning-based metrics under video attacks has not been widely studied. In addition to having success, attacks that can be employed in video processing benchmarks must be fast and imperceptible. This paper introduces an Invisible One-Iteration (IOI) adversarial attack on no reference image and video quality metrics. We compared our method alongside eight prior approaches using image a…

This https://arxiv.org/abs/2304.15000 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csPL_…

Quantum Control Machine: The Limits of Control Flow in Quantum Programming
Quantum algorithms for tasks such as factorization, search, and simulation rely on control flow such as branching and iteration that depends on the value of data in superposition. High-level programming abstractions for control flow, such as switches, loops, and higher-order functions, are ubiquitous in classical languages. By contrast, many quantum languages do not provide high-level abstractions for control flow in superposition, and instead require the use of hardware-level logic gates to im…

An extension of the Chudnovsky algorithm
John M. Campbell
https://arxiv.org/abs/2403.07291 https://arxiv.org/pdf/2403.07291

An extension of the Chudnovsky algorithm
Using an infinite family of generalizations of the Chudnovsky brothers' series recently obtained via the analytic continuation of the Borwein brothers' formula for Ramanujan-type series of level 1, we apply the Gauss-Salamin-Brent iteration for $π$ to obtain a new, Ramanujan-type series that yields more digits per term relative to current world record given by an extension of the Chudnovsky algorithm from Bagis and Glasser that produces about 110 digits per term. We explicitly evaluate the req…

This https://arxiv.org/abs/2312.14615 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

A fixed-point algorithm for matrix projections with applications in quantum information
We develop a simple fixed-point iterative algorithm that computes the matrix projection with respect to the Bures distance on the set of positive definite matrices that are invariant under some symmetry. We prove that the fixed-point iteration algorithm converges exponentially fast to the optimal solution in the number of iterations. Moreover, it numerically shows fast convergence compared to the off-the-shelf semidefinite program solvers. Our algorithm, for the specific case of matrix barycent…

This https://arxiv.org/abs/2305.17283 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Sharpened Lazy Incremental Quasi-Newton Method
The problem of minimizing the sum of $n$ functions in $d$ dimensions is ubiquitous in machine learning and statistics. In many applications where the number of observations $n$ is large, it is necessary to use incremental or stochastic methods, as their per-iteration cost is independent of $n$. Of these, Quasi-Newton (QN) methods strike a balance between the per-iteration cost and the convergence rate. Specifically, they exhibit a superlinear rate with $O(d^2)$ cost in contrast to the linear ra…

Are Targeted Messages More Effective?
Martin Grohe, Eran Rosenbluth
https://arxiv.org/abs/2403.06817 https://arxiv.org/pdf/2403.06817…

Are Targeted Messages More Effective?
Graph neural networks (GNN) are deep learning architectures for graphs. Essentially, a GNN is a distributed message passing algorithm, which is controlled by parameters learned from data. It operates on the vertices of a graph: in each iteration, vertices receive a message on each incoming edge, aggregate these messages, and then update their state based on their current state and the aggregated messages. The expressivity of GNNs can be characterised in terms of certain fragments of first-order…

IOI: Invisible One-Iteration Adversarial Attack on No-Reference Image- and Video-Quality Metrics
Ekaterina Shumitskaya, Anastasia Antsiferova, Dmitriy Vatolin
https://arxiv.org/abs/2403.05955

IOI: Invisible One-Iteration Adversarial Attack on No-Reference Image- and Video-Quality Metrics
No-reference image- and video-quality metrics are widely used in video processing benchmarks. The robustness of learning-based metrics under video attacks has not been widely studied. In addition to having success, attacks that can be employed in video processing benchmarks must be fast and imperceptible. This paper introduces an Invisible One-Iteration (IOI) adversarial attack on no reference image and video quality metrics. We compared our method alongside eight prior approaches using image a…

This https://arxiv.org/abs/2309.02826 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Vertical isomorphisms of Fedosov dg manifolds associated with a Lie pair
We investigate vertical isomorphisms of Fedosov dg manifolds associated with a Lie pair $(L,A)$, i.e. a pair of a Lie algebroid $L$ and a Lie subalgebroid $A$ of $L$. The construction of Fedosov dg manifolds involves a choice of a splitting and a connection. We prove that, given any two choices of a splitting and a connection, there exists a unique vertical isomorphism, determined by an iteration formula, between the two associated Fedosov dg manifolds. As an application, we provide an explicit…

RunPod, which offers a globally distributed GPU cloud platform for developing and deploying AI, raised a $20M seed co-led by Intel Capital and Dell Technologies (James Thomason/VentureBeat)
https://venturebeat.com/ai/exclusive-r

Exclusive: RunPod secures $20M from Dell and Intel as demand soars for AI clouds
RunPod’s platform attracts over 100,000 developers with focus on iteration speed and ease of use.

Now at their second iteration and procuring the third one, GÉANT #cloud frameworks continue to be a fundamental propelling and shaping force for #DigitalTransformation in European #Research &

How GÉANT Cloud Frameworks outline the cloudscape* of European R&E – A panoramic view | GÉANT CONNECT Online
This article is part of a section on commercial cloud procurement, published in the March 2024 issue of the GÉANT CONNECT Magazine (CONNECT45). We also suggest reading "From the OCRE project to EOSC Future - lessons learned in commercial cloud procurement". In the rapidly evolving global landscape of Research and Education, cloud-based services have become

This https://arxiv.org/abs/2305.17283 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Sharpened Lazy Incremental Quasi-Newton Method
The problem of minimizing the sum of $n$ functions in $d$ dimensions is ubiquitous in machine learning and statistics. In many applications where the number of observations $n$ is large, it is necessary to use incremental or stochastic methods, as their per-iteration cost is independent of $n$. Of these, Quasi-Newton (QN) methods strike a balance between the per-iteration cost and the convergence rate. Specifically, they exhibit a superlinear rate with $O(d^2)$ cost in contrast to the linear ra…

Diagram Analysis of Iterative Algorithms
Chris Jones, Lucas Pesenti
https://arxiv.org/abs/2404.07881 https://arxiv.org/pdf/2404.07881…

Diagram Analysis of Iterative Algorithms
We study a general class of first-order iterative algorithms which includes power iteration, belief propagation and Approximate Message Passing (AMP), and many forms of gradient descent. When the input is a random matrix with i.i.d. entries, we present a new way to analyze these algorithms using combinatorial diagrams. Each diagram is a small graph, and the operations of the algorithm correspond to simple combinatorial operations on these graphs. We prove a fundamental property of the diagram…

So #Bluesky is doing developer grants, even if very small ones. $500-$2000/project, $10k total. One thing that having a funded project lets you do.
https://bsky.app/profile/atproto.com/p

Minimax Least-Square Policy Iteration for Cost-Aware Defense of Traffic Routing against Unknown Threats
Yuzhen Zhan, Li Jin
https://arxiv.org/abs/2404.05008

Minimax Least-Square Policy Iteration for Cost-Aware Defense of Traffic Routing against Unknown Threats
Dynamic routing is one of the representative control scheme in transportation, production lines, and data transmission. In the modern context of connectivity and autonomy, routing decisions are potentially vulnerable to malicious attacks. In this paper, we consider the dynamic routing problem over parallel traffic links in the face of such threats. An attacker is capable of increasing or destabilizing traffic queues by strategic manipulating the nominally optimal routing decisions. A defender i…

This https://arxiv.org/abs/2403.00835 has been replaced.
link: https://scholar.google.com/scholar?q=a

CLLMs: Consistency Large Language Models
Parallel decoding methods such as Jacobi decoding show promise for more efficient LLM inference as it breaks the sequential nature of the LLM decoding process and transforms it into parallelizable computation. However, in practice, it achieves little speedup compared to traditional autoregressive (AR) decoding, primarily because Jacobi decoding seldom accurately predicts more than one token in a single fixed-point iteration step. To address this, we develop a new approach aimed at realizing fas…

Inexact Policy Iteration Methods for Large-Scale Markov Decision Processes
Matilde Gargiani, Robin Sieber, Efe Balta, Dominic Liao-McPherson, John Lygeros
https://arxiv.org/abs/2404.06136

Inexact Policy Iteration Methods for Large-Scale Markov Decision Processes
We consider inexact policy iteration methods for large-scale infinite-horizon discounted MDPs with finite spaces, a variant of policy iteration where the policy evaluation step is implemented inexactly using an iterative solver for linear systems. In the classical dynamic programming literature, a similar principle is deployed in optimistic policy iteration, where an a-priori fixed-number of iterations of value iteration is used to inexactly solve the policy evaluation step. Inspired by the con…

Low-rank generalized alternating direction implicit iteration method for solving matrix equations
Juan Zhang, Wenlu Xun
https://arxiv.org/abs/2404.06034 ht…

Low-rank generalized alternating direction implicit iteration method for solving matrix equations
This paper presents an effective low-rank generalized alternating direction implicit iteration (R-GADI) method for solving large-scale sparse and stable Lyapunov matrix equations and continuous-time algebraic Riccati matrix equations. The method is based on generalized alternating direction implicit iteration (GADI), which exploits the low-rank property of matrices and utilizes the Cholesky factorization approach for solving. The advantage of the new algorithm lies in its direct and efficient l…

Now at their second iteration and procuring the third one, GÉANT #cloud frameworks continue to be a fundamental propelling and shaping force for #DigitalTransformation in European #Research &

How GÉANT Cloud Frameworks outline the cloudscape* of European R&E – A panoramic view | GÉANT CONNECT Online
This article is part of a section on commercial cloud procurement, published in the March 2024 issue of the GÉANT CONNECT Magazine (CONNECT45). We also suggest reading "From the OCRE project to EOSC Future - lessons learned in commercial cloud procurement". In the rapidly evolving global landscape of Research and Education, cloud-based services have become

This https://arxiv.org/abs/2303.15237 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Cascaded variational quantum eigensolver algorithm
We present a cascaded variational quantum eigensolver algorithm that only requires the execution of a set of quantum circuits once rather than at every iteration during the parameter optimization process, thereby increasing the computational throughput. This algorithm uses a quantum processing unit to probe the needed probability mass functions and a classical processing unit perform the remaining calculations, including the energy minimization. The ansatz form does not restrict the Fock space …

An Enhanced Grey Wolf Optimizer with Elite Inheritance and Balance Search Mechanisms
Jianhua Jiang, Ziying Zhao, Weihua Li, Keqin Li
https://arxiv.org/abs/2404.06524

An Enhanced Grey Wolf Optimizer with Elite Inheritance and Balance Search Mechanisms
The Grey Wolf Optimizer (GWO) is recognized as a novel meta-heuristic algorithm inspired by the social leadership hierarchy and hunting mechanism of grey wolves. It is well-known for its simple parameter setting, fast convergence speed, and strong optimization capability. In the original GWO, there are two significant design flaws in its fundamental optimization mechanisms. Problem (1): the algorithm fails to inherit from elite positions from the last iteration when generating the next position…

The US and Saudi Arabia, according to Bloomberg News, are once again getting close to a historic pact.
But whereas its first iteration was intended as a three-way deal with Israel to isolate Iran, this version would aim just as much to pressure Israel.
Here’s the design of the entente on which the US, Saudi Arabia and Israel were converging before Hamas attacked Israel on Oct. 7:
The Saudis would make peace with Israel and forswear closer ties to China.
In return, the…

Does anybody else wish libc had an optimized "memcpy with no destination increment" routine?
In other words, for(int i=0; i<len; i ) sfr = data[i];
But optimized with loop unrolling, using full-width bus transactions rather than only doing one byte per iteration as much as possible, etc.
It's something I write all the time in embedded but I always feel like it can probably be done more efficiently and should really just be done once and librarized.

This rotary broach I designed is 1" across the (poorly) knurled section, and the body is only 34mm long. It has the minor downside of not working very well, so I get to re-make the body and nut. The spindle inside is as close to perfect as I can do, so I can keep that for the next iteration. But the next iteration will be larger in diameter which will make it easier to make. And I think no more knurling in the new design.

Fixed Point Theory Analysis of a Lambda Policy Iteration with Randomization for the \'Ciri\'c Contraction Operator
Abdelkader Belhenniche, Roman Chertovskih
https://arxiv.org/abs/2405.07824

Syndicate: Synergistic Synthesis of Ranking Function and Invariants for Termination Analysis
Yasmin Sarita, Avaljot Singh, Shaurya Gomber, Gagandeep Singh, Mahesh Vishwanathan
https://arxiv.org/abs/2404.05951

Syndicate: Synergistic Synthesis of Ranking Function and Invariants for Termination Analysis
Several techniques have been developed to prove the termination of programs. Finding ranking functions is one of the common approaches to do so. A ranking function must be bounded and must reduce at every iteration for all the reachable program states. Since the set of reachable states is often unknown, invariants serve as an over-approximation. Further, in the case of nested loops, the initial set of program states for the nested loop can be determined by the invariant of the outer loop. So, i…

An Iteration Theorem for $\omega_1$-preserving Forcings
Andreas Lietz
https://arxiv.org/abs/2403.09018 https://arxiv.org/pdf/2403.090…

An Iteration Theorem for $ω_1$-preserving Forcings
We prove an iteration theorem which guarantees for a wide class of nice iterations of $ω_1$-preserving forcings that $ω_1$ is not collapse, at the price of needing large cardinals to burn as fuel. More precisely, we show that a nice iteration of $ω_1$-preserving forcings which force SRP at successor steps and preserves old stationary sets does not collapse $ω_1$.

This https://arxiv.org/abs/2012.11748 has been replaced.
link: https://scholar.google.com/scholar?q=a

Mesh Denoising and Inpainting using the Total Variation of the Normal and a Shape Newton Approach
We present a novel approach to denoising and inpainting problems for surface meshes. The purpose of these problems is to remove noise or fill in missing parts while preserving important features such as sharp edges. A discrete variant of the total variation of the unit normal vector field serves as a regularizing functional to achieve these goals. In order to solve the resulting problem, we use a version of the split Bregman (ADMM) iteration adapted to the problem. A new formulation of the tota…

Fixed Point Theory Analysis of a Lambda Policy Iteration with Randomization for the \'Ciri\'c Contraction Operator
Abdelkader Belhenniche, Roman Chertovskih
https://arxiv.org/abs/2405.07824

This https://arxiv.org/abs/2312.11834 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csMA_…

Multi-agent reinforcement learning using echo-state network and its application to pedestrian dynamics
In recent years, simulations of pedestrians using the multi-agent reinforcement learning (MARL) have been studied. This study considered the roads on a grid-world environment, and implemented pedestrians as MARL agents using an echo-state network and the least squares policy iteration method. Under this environment, the ability of these agents to learn to move forward by avoiding other agents was investigated. Specifically, we considered two types of tasks: the choice between a narrow direct ro…

Power Series Composition in Near-Linear Time
Yasunori Kinoshita, Baitian Li
https://arxiv.org/abs/2404.05177 https://arxiv.org/pdf/24…

Power Series Composition in Near-Linear Time
We present an algebraic algorithm that computes the composition of two power series in $\mathop{\tilde{\mathrm O}}(n)$ time complexity. The previous best algorithms are $\mathop{\mathrm O}(n^{1+o(1)})$ by Kedlaya and Umans (FOCS 2008) and an $\mathop{\mathrm O}(n^{1.43})$ algebraic algorithm by Neiger, Salvy, Schost and Villard (JACM 2023). Our algorithm builds upon the recent Graeffe iteration approach to manipulate rational power series introduced by Bostan and Mori (SOSA 2021).

Adding icons for the .listStyle(.sidebar) looks too strong. Switching to .grouped does not feel great (Shown here with fake data for iteration speed).
The third one is the with icons/sidebar but fontWeight (.light)
I have a slight preference for the sidebar style more, but I am trying to manually tune fonts/colors at this point.

Advanced-Step Real-time Iterations with Four Levels -- New Error Bounds and Fast Implementation in acados
Jonathan Frey, Armin Nurkanovic, Moritz Diehl
https://arxiv.org/abs/2403.07101

Advanced-Step Real-time Iterations with Four Levels -- New Error Bounds and Fast Implementation in acados
The Real-Time Iteration (RTI) is an online nonlinear model predictive control algorithm that performs a single Sequential Quadratic Programming (SQP) per sampling time. The algorithm is split into a preparation and a feedback phase, where the latter one performs as little computations as possible solving a single prepared quadratic program. To further improve the accuracy of this method, the Advanced-Step RTI (AS-RTI) performs additional Multi-Level Iterations (MLI) in the preparation phase, su…

This https://arxiv.org/abs/2308.01243 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Quasinormal modes of the Schwarzchild black hole with a deficit solid angle and quintessence-like matter: Improved asymptotic iteration method
We study the quasinormal modes (QNM) for scalar, and electromagnetic perturbations in the Schwarzchild black hole with a deficit solid angle and quintessence-like matter. Using the sixth--order WKB approximation and the improved asymptotic iteration method (AIM) we can determine the dependence of the quasinormal modes on the parameters of the black hole and the parameters on the test fields. The values of the real part and imaginary parts of the quasi--normal modes increase with the decrease of…

An #AI I'd find really useful right now is one which filters out #MWC announcements of the form;
"Company X has announced the next iteration of Product Y which includes the headline features A, B, and C"
where A, B, and C are tiny-niche interest features that company X feel are the only…

This https://arxiv.org/abs/2012.11748 has been replaced.
link: https://scholar.google.com/scholar?q=a

Mesh Denoising and Inpainting using the Total Variation of the Normal and a Shape Newton Approach
We present a novel approach to denoising and inpainting problems for surface meshes. The purpose of these problems is to remove noise or fill in missing parts while preserving important features such as sharp edges. A discrete variant of the total variation of the unit normal vector field serves as a regularizing functional to achieve these goals. In order to solve the resulting problem, we use a version of the split Bregman (ADMM) iteration adapted to the problem. A new formulation of the tota…

Mack modes in supersonic boundary layer
Nader Masmoudi, Yuxi Wang, Di Wu, Zhifei Zhang
https://arxiv.org/abs/2405.04853 https://arxiv…

Mack modes in supersonic boundary layer
Understanding the transition mechanism of boundary layer flows is of great significance in physics and engineering, especially due to the current development of supersonic and hypersonic aircraft. In this paper, we construct multiple unstable acoustic modes so-called Mack modes, which play a crucial role during the early stage of transition in the supersonic boundary layer. To this end, we develop an inner-outer gluing iteration to solve a hyperbolic-elliptic mixed type and singular system.

The field of iterates of a rational function
Francesco Veneziano, Solomon Vishkautsan
https://arxiv.org/abs/2404.04939 https://arxiv.…

The field of iterates of a rational function
We study how the field of definition of a rational function changes under iteration. We provide a complete classification of polynomials with the property that the field of definition of one of their iterates drops in degree (over a given base field). We show with families of examples that this characterization does not hold for rational functions. Finally, we also classify fractional linear transformations with this property.

Snail: Secure Single Iteration Localization
James Choncholas, Pujith Kachana, Andr\'e Mateus, Gregoire Phillips, Ada Gavrilovska
https://arxiv.org/abs/2403.14916

Snail: Secure Single Iteration Localization
Localization is a computer vision task by which the position and orientation of a camera is determined from an image and environmental map. We propose a method for performing localization in a privacy preserving manner supporting two scenarios: first, when the image and map are held by a client who wishes to offload localization to untrusted third parties, and second, when the image and map are held separately by untrusting parties. Privacy preserving localization is necessary when the image an…

Advanced-Step Real-time Iterations with Four Levels -- New Error Bounds and Fast Implementation in acados
Jonathan Frey, Armin Nurkanovic, Moritz Diehl
https://arxiv.org/abs/2403.07101

Advanced-Step Real-time Iterations with Four Levels -- New Error Bounds and Fast Implementation in acados
The Real-Time Iteration (RTI) is an online nonlinear model predictive control algorithm that performs a single Sequential Quadratic Programming (SQP) per sampling time. The algorithm is split into a preparation and a feedback phase, where the latter one performs as little computations as possible solving a single prepared quadratic program. To further improve the accuracy of this method, the Advanced-Step RTI (AS-RTI) performs additional Multi-Level Iterations (MLI) in the preparation phase, su…

Intelligent Canvas: Enabling Design-Like Exploratory Visual Data Analysis through Rapid Prototyping, Iteration and Curation
Zijian Ding, Joel Chan
https://arxiv.org/abs/2402.08812

Intelligent Canvas: Enabling Design-Like Exploratory Visual Data Analysis through Rapid Prototyping, Iteration and Curation
Complex data analysis inherently seeks unexpected insights through exploratory \re{visual analysis} methods, transcending logical, step-by-step processing. However, \re{existing interfaces such as notebooks and dashboards have limitations in exploration and comparison for visual data analysis}. Addressing these limitations, we introduce a "design-like" intelligent canvas environment integrating generative AI into data analysis, offering rapid prototyping, iteration, and comparative visualizatio…

This https://arxiv.org/abs/2302.05855 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csRO_…

Investigation of Enhanced Inertial Navigation Algorithms by Functional Iteration
The defects of the traditional strapdown inertial navigation algorithms become well acknowledged and the corresponding enhanced algorithms have been quite recently proposed trying to mitigate both theoretical and algorithmic defects. In this paper, the analytical accuracy evaluation of both the traditional algorithms and the enhanced algorithms is investigated, against the true reference for the first time enabled by the functional iteration approach having provable convergence. The analyses by…

This https://arxiv.org/abs/2403.13245 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

Federated reinforcement learning for robot motion planning with zero-shot generalization
This paper considers the problem of learning a control policy for robot motion planning with zero-shot generalization, i.e., no data collection and policy adaptation is needed when the learned policy is deployed in new environments. We develop a federated reinforcement learning framework that enables collaborative learning of multiple learners and a central server, i.e., the Cloud, without sharing their raw data. In each iteration, each learner uploads its local control policy and the correspon…

A novel fast iterative moment method for near-continuum flows
Guanghan Li, Chunwu Wang, Zhicheng Hu
https://arxiv.org/abs/2403.07358 https://

A novel fast iterative moment method for near-continuum flows
In this paper, we develop a novel fast iterative moment method for the steady-state simulation of near-continuum flows, which are modeled by the high-order moment system derived from the Boltzmann-BGK equation. The fast convergence of the present method is mainly achieved by alternately solving the moment system and the hydrodynamic equations with compatible constitutive relations and boundary conditions. To be specific, the compatible hydrodynamic equations are solved in each iteration to get …

This https://arxiv.org/abs/2403.04259 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Decentralized and Equitable Optimal Transport
This paper considers the decentralized (discrete) optimal transport (D-OT) problem. In this setting, a network of agents seeks to design a transportation plan jointly, where the cost function is the sum of privately held costs for each agent. We reformulate the D-OT problem as a constraint-coupled optimization problem and propose a single-loop decentralized algorithm with an iteration complexity of O(1/ε) that matches existing centralized first-order approaches. Moreover, we propose the decent…

Congress should urgently reauthorize America’s key to pandemic preparedness | The Hill
https://thehill.com/opinion/healthcare/4542299-congress-should-urgently-reauthorize-americas-key-to-pandemic-preparedne…

Congress should urgently reauthorize America’s key to pandemic preparedness
The Pandemic and All-Hazards Preparedness Act has always been successfully reauthorized every five years with overwhelming bipartisan support, and this iteration should be no different.

An Iteration Theorem for $\omega_1$-preserving Forcings
Andreas Lietz
https://arxiv.org/abs/2403.09018 https://arxiv.org/pdf/2403.090…

An Iteration Theorem for $ω_1$-preserving Forcings
We prove an iteration theorem which guarantees for a wide class of nice iterations of $ω_1$-preserving forcings that $ω_1$ is not collapse, at the price of needing large cardinals to burn as fuel. More precisely, we show that a nice iteration of $ω_1$-preserving forcings which force SRP at successor steps and preserves old stationary sets does not collapse $ω_1$.

”Twenty years and two days ago, @… and I introduced #microformats in a conference presentation.“
Congrats, @…! 👏…

This https://arxiv.org/abs/2311.02557 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Fast Minimization of Expected Logarithmic Loss via Stochastic Dual Averaging
Consider the problem of minimizing an expected logarithmic loss over either the probability simplex or the set of quantum density matrices. This problem includes tasks such as solving the Poisson inverse problem, computing the maximum-likelihood estimate for quantum state tomography, and approximating positive semi-definite matrix permanents with the currently tightest approximation ratio. Although the optimization problem is convex, standard iteration complexity guarantees for first-order meth…

This https://arxiv.org/abs/2211.13566 has been replaced.
link: https://scholar.google.com/scholar?q=a

Randomized gradient-free methods in convex optimization
This review presents modern gradient-free methods to solve convex optimization problems. By gradient-free methods, we mean those that use only (noisy) realizations of the objective value. We are motivated by various applications where gradient information is prohibitively expensive or even unavailable. We mainly focus on three criteria: oracle complexity, iteration complexity, and the maximum permissible noise level.

This https://arxiv.org/abs/2208.02242 has been replaced.
link: https://scholar.google.com/scholar?q=a

Increasing-decreasing patterns in the iteration of an arithmetic function
Let $Ω$ be a set of positive integers and let $f:Ω\rightarrow Ω$ be an arithmetic function. Let $V = (v_i)_{i=1}^n$ be a finite sequence of positive integers. An integer $m \in Ω$ has \textit{increasing-decreasing pattern} $V$ with respect to $f$ if, for all odd integers $i \in \{1,\ldots, n\}$, \[ f^{v_1+ \cdots + v_{i-1}}(m) < f^{v_1+ \cdots + v_{i-1}+1}(m) < \cdots < f^{v_1+ \cdots + v_{i-1}+v_{i}}(m) \] and, for all even integers $i \in \{2,\ldots, n\}$, \[ f^{v_1+ \cdots + v_{i-1}}(m) …

Concentration Tail-Bound Analysis of Coevolutionary and Bandit Learning Algorithms
Per Kristian Lehre, Shishen Lin
https://arxiv.org/abs/2405.04480 https:/…

Concentration Tail-Bound Analysis of Coevolutionary and Bandit Learning Algorithms
Runtime analysis, as a branch of the theory of AI, studies how the number of iterations algorithms take before finding a solution (its runtime) depends on the design of the algorithm and the problem structure. Drift analysis is a state-of-the-art tool for estimating the runtime of randomised algorithms, such as evolutionary and bandit algorithms. Drift refers roughly to the expected progress towards the optimum per iteration. This paper considers the problem of deriving concentration tail-bound…

This https://arxiv.org/abs/2202.07593 has been replaced.
link: https://scholar.google.com/scholar?q=a

The dependency of spectral gaps on the convergence of the inverse iteration for a nonlinear eigenvector problem
In this paper we consider the generalized inverse iteration for computing ground states of the Gross-Pitaevskii eigenvector problem (GPE). For that we prove explicit linear convergence rates that depend on the maximum eigenvalue in magnitude of a weighted linear eigenvalue problem. Furthermore, we show that this eigenvalue can be bounded by the first spectral gap of a linearized Gross-Pitaevskii operator, recovering the same rates as for linear eigenvector problems. With this we establish the f…

Tensor Power Flow Formulations for Multidimensional Analyses in Distribution Systems
Edgar Mauricio Salazar DuqueJ.G., Juan S. GiraldoJ.G., Pedro P. VergaraJ.G., Phuong H. NguyenJ.G., HanJ.G., Slootweg
https://arxiv.org/abs/2403.04578

Tensor Power Flow Formulations for Multidimensional Analyses in Distribution Systems
In this paper, we present two multidimensional power flow formulations based on a fixed-point iteration (FPI) algorithm to efficiently solve hundreds of thousands of power flows in distribution systems. The presented algorithms are the base for a new TensorPowerFlow (TPF) tool and shine for their simplicity, benefiting from multicore \gls{cpu} and \gls{gpu} parallelization. We also focus on the mathematical convergence properties of the algorithm, showing that its unique solution is at the prac…

A preconditioned iteration method for solving saddle point problems
Juan Zhang, Yiyi Luo
https://arxiv.org/abs/2404.06061 https://arx…

A preconditioned iteration method for solving saddle point problems
This paper introduces a preconditioned method designed to comprehensively address the saddle point system with the aim of improving convergence efficiency. In the preprocessor construction phase, a technical approach for solving the approximate inverse matrix of sparse matrices is presented. The effectiveness of the proposed method is demonstrated through numerical examples, emphasizing its efficacy in approximating the inverse matrix. Furthermore, the preprocessing technology includes a low-ra…

This https://arxiv.org/abs/2102.03359 has been replaced.
link: https://scholar.google.com/scholar?q=a

Full normalization for transfinite stacks
We describe the extension of normal iteration strategies with appropriate condensation properties to strategies for stacks of normal trees, with full normalization. Given a regular uncountable cardinal $Ω$ and an $(m,Ω+1)$-iteration strategy $Σ$ for a premouse $M$, such that $Σ$ and $M$ both have appropriate condensation properties, we extend $Σ$ to a strategy $Σ^*$ for the optimal-$(m,Ω,Ω+1)^*$-iteration game such that for all $λ<Ω$ and all stacks $\vec{\mathcal{T}}=\left<\mathcal{T}…

Trust Driven On-Demand Scheme for Client Deployment in Federated Learning
Mario Chahoud, Azzam Mourad, Hadi Otrok, Jamal Bentahar, Mohsen Guizani
https://arxiv.org/abs/2405.00395 …

Trust Driven On-Demand Scheme for Client Deployment in Federated Learning
Containerization technology plays a crucial role in Federated Learning (FL) setups, expanding the pool of potential clients and ensuring the availability of specific subsets for each learning iteration. However, doubts arise about the trustworthiness of devices deployed as clients in FL scenarios, especially when container deployment processes are involved. Addressing these challenges is important, particularly in managing potentially malicious clients capable of disrupting the learning process…

This https://arxiv.org/abs/2402.08812 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csHC_…

Intelligent Canvas: Enabling Design-Like Exploratory Visual Data Analysis with Generative AI through Rapid Prototyping, Iteration and Curation
Complex data analysis inherently seeks unexpected insights through exploratory visual analysis methods, transcending logical, step-by-step processing. However, existing interfaces such as notebooks and dashboards have limitations in exploration and comparison for visual data analysis. Addressing these limitations, we introduce a "design-like" intelligent canvas environment integrating generative AI into data analysis, offering rapid prototyping, iteration, and comparative visualization manageme…

A Krylov Eigenvalue Solver Based on Filtered Time Domain Solutions
Lothar Nannen, Markus Wess
https://arxiv.org/abs/2402.08515 https://

A Krylov Eigenvalue Solver Based on Filtered Time Domain Solutions
This paper introduces a method for computing eigenvalues and eigenvectors of a generalized Hermitian, matrix eigenvalue problem. The work is focused on large scale eigenvalue problems, where the application of a direct inverse is out of reach. Instead, an explicit time-domain integrator for the corresponding wave problem is combined with a proper filtering and a Krylov iteration in order to solve for eigenvalues within a given region of interest. We report results of small scale model problems …

”Twenty years and two days ago, @… and I introduced #microformats in a conference presentation.“
Congrats, @…! 👏…

This https://arxiv.org/abs/2402.00082 has been replaced.
link: https://scholar.google.com/scholar?q=a

Enhancing Grover's Search Algorithm: A Modified Approach to Increase the Probability of Good States
This article introduces an enhancement to the Grover search algorithm to speed up computing the probability of finding good states. It suggests incorporating a rotation phase angle determined mathematically from the derivative of the model during the initial iteration. At each iteration, a new phase angle is computed and used in a rotation gate around y+z axis in the diffusion operator. The computed phase angles are optimized through an adaptive adjustment based on the estimated increasing rati…

This https://arxiv.org/abs/2310.10827 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Deep Policy Iteration for High-Dimensional Mean Field Games
This paper presents Deep Policy Iteration (DPI), a novel approach that integrates the power of Neural Networks with the stability and convergence advantages of the Policy Iteration (PI). DPI is specifically designed to address the computational complexities arising in high-dimensional stochastic Mean Field Games (MFG). Utilizing three neural networks trained iteratively, DPI adeptly approximates MFG solutions by solving PI equations and satisfying forward-backwards conditions. In contrast to PI…

Playing Games with your PET: Extending the Partial Exploration Tool to Stochastic Games
Tobias Meggendorfer, Maximilian Weininger
https://arxiv.org/abs/2405.03885

Playing Games with your PET: Extending the Partial Exploration Tool to Stochastic Games
We present version 2.0 of the Partial Exploration Tool (PET), a tool for verification of probabilistic systems. We extend the previous version by adding support for stochastic games, based on a recent unified framework for sound value iteration algorithms. Thereby, PET2 is the first tool implementing a sound and efficient approach for solving stochastic games with objectives of the type reachability/safety and mean payoff. We complement this approach by developing and implementing a partial-exp…

Square patterns in dynamical orbits
Vefa Goksel, Giacomo Micheli
https://arxiv.org/abs/2403.19642 https://arxiv.org/pdf/2403.19642

Square patterns in dynamical orbits
Let $q$ be an odd prime power. Let $f\in \mathbb{F}_q[x]$ be a polynomial having degree at least $2$, $a\in \mathbb{F}_q$, and denote by $f^n$ the $n$-th iteration of $f$. Let $χ$ be the quadratic character of $\mathbb{F}_q$, and $\mathcal{O}_f(a)$ the forward orbit of $a$ under iteration by $f$. Suppose that the sequence $(χ(f^n(a)))_{n\geq 1}$ is periodic, and $m$ is its period. Assuming a mild and generic condition on $f$, we show that, up to a constant, $m$ can be bounded from below by $&…

This https://arxiv.org/abs/2102.03359 has been replaced.
link: https://scholar.google.com/scholar?q=a

Full normalization for transfinite stacks
We describe the extension of normal iteration strategies with appropriate condensation properties to strategies for stacks of normal trees, with full normalization. Given a regular uncountable cardinal $Ω$ and an $(m,Ω+1)$-iteration strategy $Σ$ for a premouse $M$, such that $Σ$ and $M$ both have appropriate condensation properties, we extend $Σ$ to a strategy $Σ^*$ for the optimal-$(m,Ω,Ω+1)^*$-iteration game such that for all $λ<Ω$ and all stacks $\vec{\mathcal{T}}=\left<\mathcal{T}…

Convergence of a Ramshaw-Mesina Iteration
Aytekin \c{C}ibik, William Layton
https://arxiv.org/abs/2403.04702 https://arxiv.org/pdf/24…

Convergence of a Ramshaw-Mesina Iteration
In 1991 Ramshaw and Mesina introduced a clever synthesis of penalty methods and artificial compression methods. Its form makes it an interesting option to replace the pressure update in the Uzawa iteration. The result, for the Stokes problem, is \begin{equation} \left\{ \begin{array} [c]{cc} Step\ 1: & -\triangle u^{n+1}+\nabla p^{n}=f(x),\ {\rm in}\ Ω,\ u^{n+1}|_{\partialΩ}=0,\\ Step\ 2: & p^{n+1}-p^{n}+β\nabla\cdot(u^{n+1}-u^{n})+α^{2}\nabla\cdot u^{n+1}=0. \end{array} \right. \end{e…

This https://arxiv.org/abs/2307.08429 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Global convergence of a BFGS-type algorithm for nonconvex multiobjective optimization problems
We propose a modified BFGS algorithm for multiobjective optimization problems with global convergence, even in the absence of convexity assumptions on the objective functions. Furthermore, we establish the superlinear convergence of the method under usual conditions. Our approach employs Wolfe step sizes and ensures that the Hessian approximations are updated and corrected at each iteration to address the lack of convexity assumption. Numerical results shows that the introduced modifications pr…

This https://arxiv.org/abs/2402.01275 has been replaced.
link: https://scholar.google.com/scholar?q=a

Parametric-Task MAP-Elites
Optimizing a set of functions simultaneously by leveraging their similarity is called multi-task optimization. Current black-box multi-task algorithms only solve a finite set of tasks, even when the tasks originate from a continuous space. In this paper, we introduce Parametric-Task MAP-Elites (PT-ME), a new black-box algorithm for continuous multi-task optimization problems. This algorithm (1) solves a new task at each iteration, effectively covering the continuous space, and (2) exploits a ne…

We are excited to announce the publication of the #OCRE2024 Tender for the large-scale procurement of commercial #cloud services offerings for our pan-European #Research and

GÉANT announces publication of OCRE 2024 tender for pan-European cloud services procurement | GÉANT CONNECT Online
21 March 2024. GÉANT is delighted to announce the publication of the OCRE 2024 Tender for the large-scale procurement of commercial cloud services offerings for its pan-European Research and Education community. The tender aims to procure the OCRE 2024 Cloud framework agreements - the third iteration of GÉANT’s flagship cloud frameworks that since 2016 have

This https://arxiv.org/abs/2302.08581 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Abstract Corrected Iterations
We consider $(<λ)$-support iterations of $(<λ)$-strategically complete $λ^+$-c.c. definable forcing notions along partial orders. We show that such iterations can be corrected to yield an analog of a result by Judah and Shelah for finite support iterations of Suslin ccc forcing, namely that if $(\mathbb{P}_α, \underset{\sim}{\mathbb Q_β} : α\leq δ, β<δ)$ is a FS iteration of Suslin ccc forcing and $U\subseteq δ$ is sufficiently closed, then letting $\mathbb{P}_U$ be the iteration alon…

This https://arxiv.org/abs/2402.08812 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csHC_…

Intelligent Canvas: Enabling Design-Like Exploratory Visual Data Analysis through Rapid Prototyping, Iteration and Curation
Complex data analysis inherently seeks unexpected insights through exploratory \re{visual analysis} methods, transcending logical, step-by-step processing. However, \re{existing interfaces such as notebooks and dashboards have limitations in exploration and comparison for visual data analysis}. Addressing these limitations, we introduce a "design-like" intelligent canvas environment integrating generative AI into data analysis, offering rapid prototyping, iteration, and comparative visualizatio…

Numerical analysis of small-strain elasto-plastic deformation using local Radial Basis Function approximation with Picard iteration
Filip Strni\v{s}a, Mitja Jan\v{c}i\v{c}, Gregor Kosec
https://arxiv.org/abs/2405.04970

Numerical analysis of small-strain elasto-plastic deformation using local Radial Basis Function approximation with Picard iteration
This paper deals with a numerical analysis of plastic deformation under various conditions, utilizing Radial Basis Function (RBF) approximation. The focus is on the elasto-plastic von Mises problem under plane-strain assumption. Elastic deformation is modelled using the Navier-Cauchy equation. In regions where the von Mises stress surpasses the yield stress, corrections are applied locally through a return mapping algorithm. The non-linear deformation problem in the plastic domain is solved usi…

This https://arxiv.org/abs/2302.08581 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Abstract Corrected Iterations
We consider $(<λ)$-support iterations of $(<λ)$-strategically complete $λ^+$-c.c. definable forcing notions along partial orders. We show that such iterations can be corrected to yield an analog of a result by Judah and Shelah for finite support iterations of Suslin ccc forcing, namely that if $(\mathbb{P}_α, \underset{\sim}{\mathbb Q_β} : α\leq δ, β<δ)$ is a FS iteration of Suslin ccc forcing and $U\subseteq δ$ is sufficiently closed, then letting $\mathbb{P}_U$ be the iteration alon…

This https://arxiv.org/abs/2211.02780 has been replaced.
link: https://scholar.google.com/scholar?q=a

Flexible-step Model Predictive Control based on Generalized Lyapunov Functions
We present a novel nonlinear model predictive control (MPC) scheme with relaxed stability criteria, based on the idea of generalized discrete-time control Lyapunov functions. These functions need to satisfy an average descent over a finite window of time, rather than a descent at every time step. One feature of this scheme is that it allows for implementing a flexible number of control inputs in each iteration, in a computationally attractive manner, while guaranteeing recursive feasibility and…

This https://arxiv.org/abs/2011.01718 has been replaced.
link: https://scholar.google.com/scholar?q=a

Multi-Iteration Stochastic Optimizers
We here introduce Multi-Iteration Stochastic Optimizers, a novel class of first-order stochastic optimizers where the relative $L^2$ error is estimated and controlled using successive control variates along the path of iterations. By exploiting the correlation between iterates, control variates may reduce the estimator's variance so that an accurate estimation of the mean gradient becomes computationally affordable. We name the estimator of the mean gradient Multi-Iteration stochastiC Estimator…

This https://arxiv.org/abs/2307.12615 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Finite-sum optimization: Adaptivity to smoothness and loopless variance reduction
For finite-sum optimization, variance-reduced gradient methods (VR) compute at each iteration the gradient of a single function (or of a mini-batch), and yet achieve faster convergence than SGD thanks to a carefully crafted lower-variance stochastic gradient estimator that reuses past gradients. Another important line of research of the past decade in continuous optimization is the adaptive algorithms such as AdaGrad, that dynamically adjust the (possibly coordinate-wise) learning rate to past …

Preprocessed GMRES for fast solution of linear equations
Juan Zhang, Yiyi Luo
https://arxiv.org/abs/2404.06018 https://arxiv.org/pdf/…

Preprocessed GMRES for fast solution of linear equations
The article mainly introduces preprocessing algorithms for solving linear equation systems. This algorithm uses three algorithms as inner iterations, namely RPCG algorithm, ADI algorithm, and Kaczmarz algorithm. Then, it uses BA-GMRES as an outer iteration to solve the linear equation system. These three algorithms can indirectly generate preprocessing matrices, which are used for solving equation systems. In addition, we provide corresponding convergence analysis and numerical examples. Throug…

This https://arxiv.org/abs/2404.02635 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

An Inexact Regularized Proximal Newton Method without Line Search
In this paper, we introduce an inexact regularized proximal Newton method (IRPNM) that does not require any line search. The method is designed to minimize the sum of a twice continuously differentiable function $f$ and a convex (possibly non-smooth and extended-valued) function $φ$. Instead of controlling a step size by a line search procedure, we update the regularization parameter in a suitable way, based on the success of the previous iteration. The global convergence of the sequence of it…

Notes on the coexistence of limit notions
Takashi Yamazoe
https://arxiv.org/abs/2402.17321 https://arxiv.org/pdf/2402.17321

Notes on the coexistence of limit notions
We summarize the current knowledge on the three limit notions: ultrafilter-limits, closed-ultrafilter-limits and FAM-limits. Also, we consider the possibility to perform an iteration which has all the three limits and clarify the problem we face.

This https://arxiv.org/abs/2312.00463 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Low-rank-modified Galerkin methods for the Lyapunov equation
Of all the possible projection methods for solving large-scale Lyapunov matrix equations, Galerkin approaches remain much more popular than minimal-residual ones. This is mainly due to the different nature of the projected problems stemming from these two families of methods. While a Galerkin approach leads to the solution of a low-dimensional matrix equation per iteration, a matrix least-squares problem needs to be solved per iteration in a minimal-residual setting. The significant computation…

This https://arxiv.org/abs/2403.15749 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Horoballs and the subgradient method
To explore convex optimization on Hadamard spaces, we consider an iteration in the style of a subgradient algorithm. Traditionally, such methods assume that the underlying spaces are manifolds and that the objectives are geodesically convex: the methods are described using tangent spaces and exponential maps. By contrast, our iteration applies in a general Hadamard space, is framed in the underlying space itself, and relies instead on horospherical convexity of the objective level sets. For thi…

This https://arxiv.org/abs/2211.08212 has been replaced.
link: https://scholar.google.com/scholar?q=a

A Homogeneous Second-Order Descent Method for Nonconvex Optimization
In this paper, we introduce a Homogeneous Second-Order Descent Method (HSODM) using the homogenized quadratic approximation to the original function. The merit of homogenization is that only the leftmost eigenvector of a gradient-Hessian integrated matrix is computed at each iteration. Therefore, the algorithm is a single-loop method that does not need to switch to other sophisticated algorithms and is easy to implement. We show that HSODM has a global convergence rate of $O(ε^{-3/2})$ to find…

This https://arxiv.org/abs/2101.09180 has been replaced.
link: https://scholar.google.com/scholar?q=a

A Newton's Iteration Converges Quadratically to Nonisolated Solutions Too
The textbook Newton's iteration is practically inapplicable on solutions of nonlinear systems with singular Jacobians. By a simple modification, a novel extension of Newton's iteration regains its local quadratic convergence toward nonisolated solutions that are semiregular as properly defined regardless of whether the system is square, underdetermined or overdetermined while Jacobians can be rank-deficient. Furthermore, the iteration serves as a regularization mechanism for computing singular …

Analysis of the Picard-Newton iteration for the Navier-Stokes equations: global stability and quadratic convergence
Sara Pollock, Leo Rebholz, Xuemin Tu, Menyging Xiao
https://arxiv.org/abs/2402.12304

Analysis of the Picard-Newton iteration for the Navier-Stokes equations: global stability and quadratic convergence
We analyze and test a simple-to-implement two-step iteration for the incompressible Navier-Stokes equations that consists of first applying the Picard iteration and then applying the Newton iteration to the Picard output. We prove that this composition of Picard and Newton converges quadratically, and our analysis (which covers both the unique solution and non-unique solution cases) also suggests that this solver has a larger convergence basin than usual Newton because of the improved stability…

This https://arxiv.org/abs/2305.00424 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Policy Iteration Reinforcement Learning Method for Continuous-time Mean-Field Linear-Quadratic Optimal Problem
This paper employs a policy iteration reinforcement learning (RL) method to study continuous-time linear quadratic mean-field control problems in the infinite horizon. The drift and diffusion terms in the dynamics involve the state as well as the control. We investigate the stability and convergence of the RL algorithm using a Lyapunov Recursion. Instead of solving a pair of coupled Riccati equations, the RL technique focuses on strengthening an auxiliary function and the cost functional as the…

This https://arxiv.org/abs/2211.05463 has been replaced.
link: https://scholar.google.com/scholar?q=a

Stability and Convergence of a Randomized Model Predictive Control Strategy
RBM-MPC is a computationally efficient variant of Model Predictive Control (MPC) in which the Random Batch Method (RBM) is used to speed up the finite-horizon optimal control problems at each iteration. In this paper, stability and convergence estimates are derived for RBMMPC of unconstrained linear systems. The obtained estimates are validated in a numerical example that also shows a clear computational advantage of RBM-MPC.

Quantitative asymptotic regularity of the VAM iteration with error terms for accretive operators in Banach spaces
Paulo Firmino, Laurentiu Leustean
https://arxiv.org/abs/2402.17947

Quantitative asymptotic regularity of the VAM iteration with error terms for accretive operators in Banach spaces
In this paper we obtain, by using proof mining methods, quantitative results on the asymptotic regularity of the viscosity approximation method (VAM) with error terms for accretive operators in Banach spaces. For concrete instances of the parameter sequences, linear rates are computed by applying a lemma due to Sabach and Shtern.

This https://arxiv.org/abs/2402.17947 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Quantitative asymptotic regularity of the VAM iteration with error terms for accretive operators in Banach spaces
In this paper we obtain, by using proof mining methods, quantitative results on the asymptotic regularity of the viscosity approximation method (VAM) with error terms for accretive operators in Banach spaces. For concrete instances of the parameter sequences, linear rates are computed by applying a lemma due to Sabach and Shtern.

This https://arxiv.org/abs/2401.00778 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Convergence analysis of Lawson's iteration for the polynomial and rational minimax approximations
Lawson's iteration is a classical and effective method for solving the linear (polynomial) minimax approximation in the complex plane. Extension of Lawson's iteration for the rational minimax approximation with both computationally high efficiency and theoretical guarantee is challenging. A recent work [L.-H. Zhang, L. Yang, W. H. Yang and Y.-N. Zhang, A convex dual programming for the rational minimax approximation and Lawson's iteration, 2023, arXiv:2308.06991v1] reveals that Lawson's iterati…

This https://arxiv.org/abs/2206.13090 has been replaced.
link: https://scholar.google.com/scholar?q=a

Variance Reduced Random Relaxed Projection Method for Constrained Finite-sum Minimization Problems
For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to efficiently solve this problem. Compared with existing RPMs, our proposed algorithm features two useful algorithmic ideas. First, at each iteration, instead of projecting onto the subset defined by one of the constraints, our algorithm only requires projecti…

Dynamically accelerating the power iteration with momentum
Christian Austin, Sara Pollock, Yunrong Zhu
https://arxiv.org/abs/2403.09618 https://

Dynamically accelerating the power iteration with momentum
In this paper, we propose, analyze and demonstrate a dynamic momentum method to accelerate power and inverse power iterations with minimal computational overhead. The method is appropriate for real, diagonalizable matrices, and does not require a priori spectral knowledge. We review and extend background results on previously developed static momentum accelerations for the power iteration through the connection between the momentum accelerated iteration and the standard power iteration applied …

This https://arxiv.org/abs/2307.00276 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On convergence of waveform relaxation for nonlinear systems of ordinary differential equations
To integrate large systems of nonlinear differential equations in time, we consider a variant of nonlinear waveform relaxation (also known as dynamic iteration or Picard-Lindelöf iteration), where at each iteration a linear inhomogeneous system of differential equations has to be solved. This is done by the exponential block Krylov subspace (EBK) method. Thus, we have an inner-outer iterative method, where iterative approximations are determined over a certain time interval, with no time stepp…

Inexact Adaptive Cubic Regularization Algorithms on Riemannian Manifolds and Application
Z. Y. Li, X. M. Wang
https://arxiv.org/abs/2405.02588 https://

Inexact Adaptive Cubic Regularization Algorithms on Riemannian Manifolds and Application
The adaptive cubic regularization algorithm employing the inexact gradient and Hessian is proposed on general Riemannian manifolds, together with the iteration complexity to get an approximate second-order optimality under certain assumptions on accuracies about the inexact gradient and Hessian. The algorithm extends the inexact adaptive cubic regularization algorithm under true gradient in [Math. Program., 184(1-2): 35-70, 2020] to more general cases even in Euclidean settings. As an applicati…

This https://arxiv.org/abs/2402.05415 has been replaced.
link: https://scholar.google.com/scholar?q=a

Near-Optimal Convex Simple Bilevel Optimization with a Bisection Method
This paper studies a class of simple bilevel optimization problems where we minimize a composite convex function at the upper-level subject to a composite convex lower-level problem. Existing methods either provide asymptotic guarantees for the upper-level objective or attain slow sublinear convergence rates. We propose a bisection algorithm to find a solution that is $ε_f$-optimal for the upper-level objective and $ε_g$-optimal for the lower-level objective. In each iteration, the binary sea…

This https://arxiv.org/abs/2403.12338 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Stochastic Halpern iteration in normed spaces and applications to reinforcement learning
We analyze the oracle complexity of the stochastic Halpern iteration with variance reduction, where we aim to approximate fixed-points of nonexpansive and contractive operators in a normed finite-dimensional space. We show that if the underlying stochastic oracle is with uniformly bounded variance, our method exhibits an overall oracle complexity of $\tilde{O}(\varepsilon^{-5})$, improving recent rates established for the stochastic Krasnoselskii-Mann iteration. Also, we establish a lower bound…

This https://arxiv.org/abs/2403.12338 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Stochastic Halpern iteration in normed spaces and applications to reinforcement learning
We analyze the oracle complexity of the stochastic Halpern iteration with variance reduction, where we aim to approximate fixed-points of nonexpansive and contractive operators in a normed finite-dimensional space. We show that if the underlying stochastic oracle is with uniformly bounded variance, our method exhibits an overall oracle complexity of $\tilde{O}(\varepsilon^{-5})$, improving recent rates established for the stochastic Krasnoselskii-Mann iteration. Also, we establish a lower bound…

An Inexact Regularized Proximal Newton Method without Line Search
Simeon vom Dahl, Christian Kanzow
https://arxiv.org/abs/2404.02635 https://

An Inexact Regularized Proximal Newton Method without Line Search
In this paper, we introduce an inexact regularized proximal Newton method (IRPNM) that does not require any line search. The method is designed to minimize the sum of a twice continuously differentiable function $f$ and a convex (possibly non-smooth and extended-valued) function $φ$. Instead of controlling a step size by a line search procedure, we update the regularization parameter in a suitable way, based on the success of the previous iteration. The global convergence of the sequence of it…