Tootfinder

Flexible fixed-point iteration and its applications for nonsymmetric algebraic Riccati equations
Zhen-Chen Guo, Xin Liang
https://arxiv.org/abs/2509.25942 https://

Flexible fixed-point iteration and its applications for nonsymmetric algebraic Riccati equations
In this paper, we reveal the intrinsic Toeplitz structure in the unique stabilizing solution for nonsymmetric algebraic Riccati equations by employing a shift-involved fixed-point iteration, and propose an RADI-type method for computing this solution for large-scale equations of this type with sparse and low-rank structure by incorporating flexible shifts into the fixed-point iteration. We present a shift-selection strategy, termed Leja shifts, based on rational approximation theory, which is i…

A Block-Activated Decomposition Algorithm for Multi-Stage Stochastic Variational Inequalities
Minh N. B\`ui
https://arxiv.org/abs/2509.26198 https://arxiv.…

A Block-Activated Decomposition Algorithm for Multi-Stage Stochastic Variational Inequalities
We develop a block-activated decomposition algorithm for multi-stage stochastic variational inequalities with nonanticipativity constraints, which offers two computational novelties: (i) At each iteration, our method activates only a user-chosen block of scenarios. (ii) For each activated scenario, it employs the resolvent of the cost operator and the projector onto the constraint set separately. These features enhance computational tractability, in contrast with existing approaches, which ofte…

Wohoo, QGIS Arrow support has been merged: https://github.com/qgis/QGIS/pull/63749
Thanks @… & @…

Implement QgsArrowIterator to iterate over features as batches of ArrowArray by paleolimbot · Pull Request #63749 · qgis/QGIS
Description As encouraged by @nyalldawson! https://mastodon.social/@nyalld/115459416976982489 The motivation is to eliminate the need for per-feature iteration in Python to maintain the fidelity of...

Locally Lipschitz Path Dependent FBSDEs with Unbounded Terminal Conditions in Brownian and L{\'e}vy Settings
Hannah Geiss (JYU), C\'eline Labart (LAMA), Adrien Richou (IMB), Alexander Steinicke
https://arxiv.org/abs/2509.26423

Locally Lipschitz Path Dependent FBSDEs with Unbounded Terminal Conditions in Brownian and L{é}vy Settings
This paper is dedicated to the analysis of forward backward stochastic differential equations driven by a L{é}vy process. We assume that the generator and the terminal condition are path-dependent and satisfy a local Lipschitz condition. We study solvability and Malliavin differentiability of such BSDEs. The proof of the existence and uniqueness is done in three steps. First of all, we truncate and localize the terminal condition and the generator. Then we use an iteration argument to get boun…

Global Optimization Algorithm for Mixed-Integer Nonlinear Programs with Trigonometric Functions
Christopher Montez, Sujeevraja Sanjeevi, Kaarthik Sundar
https://arxiv.org/abs/2509.26516

Global Optimization Algorithm for Mixed-Integer Nonlinear Programs with Trigonometric Functions
This article presents the first mixed-integer linear programming (MILP)-based iterative algorithm to solve factorable mixed-integer nonlinear programs (MINLPs) with bounded, differentiable periodic functions to global optimality with an emphasis on trigonometric functions. At each iteration, the algorithm solves a MILP relaxation of the original MINLP to obtain a bound on the optimal objective value. The relaxations are constructed using partitions of variables involved in each nonlinear term a…

⚡ MXene current collectors could reduce size and improve recyclability of Li-ion batteries
https://techxplore.com/news/2025-10-mxene-current-collectors-size-recyclability.html

MXene current collectors could reduce size and improve recyclability of Li-ion batteries
The vast majority of consumer electronics use lithium-ion batteries, and with each generation, these devices are designed smaller, lighter and with longer battery life to meet the growing demands of consumers. Each new iteration also brings the batteries that power the devices closer to the limits of their size, weight and performance.

Correlating Cross-Iteration Noise for DP-SGD using Model Curvature
Xin Gu, Yingtai Xiao, Guanlin He, Jiamu Bai, Daniel Kifer, Kiwan Maeng
https://arxiv.org/abs/2510.05416 https:…

Correlating Cross-Iteration Noise for DP-SGD using Model Curvature
Differentially private stochastic gradient descent (DP-SGD) offers the promise of training deep learning models while mitigating many privacy risks. However, there is currently a large accuracy gap between DP-SGD and normal SGD training. This has resulted in different lines of research investigating orthogonal ways of improving privacy-preserving training. One such line of work, known as DP-MF, correlates the privacy noise across different iterations of stochastic gradient descent -- allowing l…

To ChatGPT: List the implant dates of human recipients of a Neuralink brain implant https://chatgpt.com/share/68f4b806-b23c-8004-a18c-30f31a4ba71f "For a company like Neuralink, whose entire value proposition hinges on rapid iteration and scale, a pause of six-plus w…

ChatGPT - Neuralink implant dates
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"For Levy and Newborn, the stakes were clear, and the title of the first chapter of the book says it all: “The Challenge is World Champion Kasparov”. Said chapter describes in detail the match between a first iteration of a chess supercomputer by IBM, the less well-known “Deep Thought”. It was a strong contender, having defeated quite a few grandmasters along the way (including the aforementioned Levy), but was no match for Kasparov in August 1989."

David Levy & Monty Newborn
The literature about and around chess is too long to enumerate in an article of a thousand words, and this is clearly not my intent. If you want to learn chess, there are so many good books around, it is hard to pick just one. There are, however, fewer books explaining the art of how to teach a computer to play chess; and the one chosen for this issue of the Library section does a magnificent job at precisely that.

An efficient iteration method to reconstruct the drift term from the final measurement
Dakang Cen, Wenlong Zhang, Zhidong Zhang
https://arxiv.org/abs/2510.10940 https://

An efficient iteration method to reconstruct the drift term from the final measurement
This work investigates the inverse drift problem in the one-dimensional parabolic equation with the final time data. The authors construct an operator first, whose fixed points are the unknown drift, and then apply it to prove the uniqueness. The proof of uniqueness contains an iteration converging to the drift, which inspires the numerical algorithm. To handle the ill-posedness of the inverse problem, the authors add the mollification on the data first in the iterative algorithm, and then prov…

Digital ID – The New Chains of Capitalist Surveillance
[…] From passports to colonial passbooks, from welfare cards to border regimes, the apparatus of identification has always been tied to domination. Digital ID is simply the latest iteration of this long history, but with a scale and sophistication that makes its dangers even more profound. […]
👷

Digital ID – The New Chains of Capitalist Surveillance - Aotearoa Workers Solidarity Movement
The world is entering an era where identity is no longer a matter of personal relationships, lived experience, or even paperwork. Increasingly, it is reduced...

Love it when someone finally responds to me after literally months of silence, I ask a question and they respond correcting me and saying they've taken action now anyway "to avoid further iteration and delay".

I made a #HamRadio antenna that I really like, and wanted to share the design and process so others can do it too. It's a carefully-tuned linked dipole that is light and has served me well for #POTA activations. It's now in its second iteration and so far I'm very happy with it.
…

«at this point, AT Proto has become essentially a sort of ideological vaporware; a way for Jay Graber et al to run a social media platform while claiming they don't run a social media platform. This is, of course, just another iteration of the Silicon Valley monoproduct: power without accountability.»
Delusions of a Protocol | Azhdarchid
#bluesky

Promptimizer: User-Led Prompt Optimization for Personal Content Classification
Leijie Wang, Kathryn Yurechko, Amy X. Zhang
https://arxiv.org/abs/2510.09009 https://

Promptimizer: User-Led Prompt Optimization for Personal Content Classification
While LLMs now enable users to create content classifiers easily through natural language, automatic prompt optimization techniques are often necessary to create performant classifiers. However, such techniques can fail to consider how social media users want to evolve their filters over the course of usage, including desiring to steer them in different ways during initialization and iteration. We introduce a user-centered prompt optimization technique, Promptimizer, that maintains high perform…

https://web.archive.org/web/20050323234233/http://www.isdickcheneydeadyet.com/
This is the last known iteration of the website “isdickcheneydeadyet.com”, from March 2005. This is when it had a blog format, and continued as a dead site until the end …

An Improved Quantum Algorithm for 3-Tuple Lattice Sieving
Lynn Engelberts, Yanlin Chen, Amin Shiraz Gilani, Maya-Iggy van Hoof, Stacey Jeffery, Ronald de Wolf
https://arxiv.org/abs/2510.08473

An Improved Quantum Algorithm for 3-Tuple Lattice Sieving
The assumed hardness of the Shortest Vector Problem in high-dimensional lattices is one of the cornerstones of post-quantum cryptography. The fastest known heuristic attacks on SVP are via so-called sieving methods. While these still take exponential time in the dimension $d$, they are significantly faster than non-heuristic approaches and their heuristic assumptions are verified by extensive experiments. $k$-Tuple sieving is an iterative method where each iteration takes as input a large numbe…

Low Complexity Detector for XL-MIMO Uplink: A Cross Splitting Based Information Geometry Approach
Wenjun Zhang, An-An Lu, Xiqi Gao
https://arxiv.org/abs/2510.09039 https://

Low Complexity Detector for XL-MIMO Uplink: A Cross Splitting Based Information Geometry Approach
In this paper, we propose the cross splitting based information geometry approach (CS-IGA), a novel and low complexity iterative detector for uplink signal recovery in extralarge-scale MIMO (XL-MIMO) systems. Conventional iterative detectors, such as the approximate message passing (AMP) algorithm and the traditional information geometry algorithm (IGA), suffer from a per iteration complexity that scales with the number of base station (BS) antennas, creating a computational bottleneck. To over…

Implicit Updates for Average-Reward Temporal Difference Learning
Hwanwoo Kim, Dongkyu Derek Cho, Eric Laber
https://arxiv.org/abs/2510.06149 https://arxiv.…

Implicit Updates for Average-Reward Temporal Difference Learning
Temporal difference (TD) learning is a cornerstone of reinforcement learning. In the average-reward setting, standard TD($λ$) is highly sensitive to the choice of step-size and thus requires careful tuning to maintain numerical stability. We introduce average-reward implicit TD($λ$), which employs an implicit fixed point update to provide data-adaptive stabilization while preserving the per iteration computational complexity of standard average-reward TD($λ$). In contrast to prior finite-tim…

GAR: Generative Adversarial Reinforcement Learning for Formal Theorem Proving
Ruida Wang, Jiarui Yao, Rui Pan, Shizhe Diao, Tong Zhang
https://arxiv.org/abs/2510.11769 https://

GAR: Generative Adversarial Reinforcement Learning for Formal Theorem Proving
Solving math problems through verifiable languages such as Lean has significantly impacted both the mathematics and computer science communities. Current state-of-the-art models are often trained with expensive online Reinforcement Learning (RL) or expert iteration. However, these approaches rely on fixed problem sets, which causes inefficient training and limits the model to tackle complex problems. To overcome these limitations, we propose GAR: Generative Adversarial Reinforcement learning, a…

Cocoon: A System Architecture for Differentially Private Training with Correlated Noises
Donghwan Kim, Xin Gu, Jinho Baek, Timothy Lo, Younghoon Min, Kwangsik Shin, Jongryool Kim, Jongse Park, Kiwan Maeng
https://arxiv.org/abs/2510.07304

Cocoon: A System Architecture for Differentially Private Training with Correlated Noises
Machine learning (ML) models memorize and leak training data, causing serious privacy issues to data owners. Training algorithms with differential privacy (DP), such as DP-SGD, have been gaining attention as a solution. However, DP-SGD adds a noise at each training iteration, which degrades the accuracy of the trained model. To improve accuracy, a new family of approaches adds carefully designed correlated noises, so that noises cancel out each other across iterations. We performed an extensive…

A Frank-Wolfe Algorithm for Strongly Monotone Variational Inequalities
Reza Rahimi Baghbadorani, Peyman Mohajerin Esfahani, Sergio Grammatico
https://arxiv.org/abs/2510.03842 ht…

A Frank-Wolfe Algorithm for Strongly Monotone Variational Inequalities
We propose an accelerated algorithm with a Frank-Wolfe method as an oracle for solving strongly monotone variational inequality problems. While standard solution approaches, such as projected gradient descent (aka value iteration), involve projecting onto the desired set at each iteration, a distinctive feature of our proposed method is the use of a linear minimization oracle in each iteration. This difference potentially reduces the projection cost, a factor that can become significant for cer…

Outer length billiards on a large scale
Peter Albers, Lael Edwards-Costa, Serge Tabachnikov
https://arxiv.org/abs/2510.08370 https://arxiv.org/pdf/2510.083…

Outer length billiards on a large scale
We present some foundational results about the outer length billiard system, including its generating function and the invariant area form. We describe the limiting behavior of the orbits far away from the billiard table: the orbits of the map lie on the origin-centered circles, and the second iteration of the map is approximated by the flow of a Hamiltonian function whose level curves are these circles. Furthermore, the orbits "at infinity" of the centers of the auxiliary circles involved in t…

Harnessing the XMM-Newton data: X-ray spectral modelling of 4XMM-DR11 detections and 4XMM-DR11s sources
A. Viitanen, G. Mountrichas, H. Stiele, F. J. Carrera, A. Ruiz, J. Ballet, A. Akylas, A. Corral, M. Freyberg, A. Georgakakis, I. Georgantopoulos, S. Mateos, C. Motch, A. Nebot, H. Tranin, N. Webb
https://arxiv.org/abs/2510.03409

Harnessing the XMM-Newton data: X-ray spectral modelling of 4XMM-DR11 detections and 4XMM-DR11s sources
The XMM-Newton X-ray observatory has played a prominent role in astrophysics, conducting precise and thorough observations of the X-ray sky for the past two decades. The most recent iteration of the 4XMM catalogue and one of its latest data releases DR11 mark significant improvements over previous XMM-Newton catalogues, serving as a cornerstone for comprehending the diverse inhabitants of the X-ray sky. We employ detections and spectra extracted from the 4XMM-DR11 catalogue, subjecting them to …

Improved $\ell_{p}$ Regression via Iteratively Reweighted Least Squares
Alina Ene, Ta Duy Nguyen, Adrian Vladu
https://arxiv.org/abs/2510.01729 https://arx…

Improved $\ell_{p}$ Regression via Iteratively Reweighted Least Squares
We introduce fast algorithms for solving $\ell_{p}$ regression problems using the iteratively reweighted least squares (IRLS) method. Our approach achieves state-of-the-art iteration complexity, outperforming the IRLS algorithm by Adil-Peng-Sachdeva (NeurIPS 2019) and matching the theoretical bounds established by the complex algorithm of Adil-Kyng-Peng-Sachdeva (SODA 2019, J. ACM 2024) via a simpler lightweight iterative scheme. This bridges the existing gap between theoretical and practical a…

Off-Policy Reinforcement Learning with Anytime Safety Guarantees via Robust Safe Gradient Flow
Pol Mestres, Arnau Marzabal, Jorge Cort\'es
https://arxiv.org/abs/2510.01492 h…

Off-Policy Reinforcement Learning with Anytime Safety Guarantees via Robust Safe Gradient Flow
This paper considers the problem of solving constrained reinforcement learning (RL) problems with anytime guarantees, meaning that the algorithmic solution must yield a constraint-satisfying policy at every iteration of its evolution. Our design is based on a discretization of the Robust Safe Gradient Flow (RSGF), a continuous-time dynamics for anytime constrained optimization whose forward invariance and stability properties we formally characterize. The proposed strategy, termed RSGF-RL, is a…

https://web.archive.org/web/20050323234233/http://www.isdickcheneydeadyet.com/
This is the last known iteration of the website “isdickcheneydeadyet.com”, from March 2005. This is when it had a blog format, and continued as a dead site until the end …

A Warm-basis Method for Bridging Learning and Iteration: a Case Study in Fluorescence Molecular Tomography
Ruchi Guo, Jiahua Jiang, Bangti Jin, Wuwei Ren, Jianru Zhang
https://arxiv.org/abs/2510.05926 …

A Warm-basis Method for Bridging Learning and Iteration: a Case Study in Fluorescence Molecular Tomography
Fluorescence Molecular Tomography (FMT) is a widely used non-invasive optical imaging technology in biomedical research. It usually faces significant accuracy challenges in depth reconstruction, and conventional iterative methods struggle with poor $z$-resolution even with advanced regularization. Supervised learning approaches can improve recovery accuracy but rely on large, high-quality paired training dataset that is often impractical to acquire in practice. This naturally raises the questio…

The Potential of Second-Order Optimization for LLMs: A Study with Full Gauss-Newton
Natalie Abreu, Nikhil Vyas, Sham Kakade, Depen Morwani
https://arxiv.org/abs/2510.09378 https…

The Potential of Second-Order Optimization for LLMs: A Study with Full Gauss-Newton
Recent efforts to accelerate LLM pretraining have focused on computationally-efficient approximations that exploit second-order structure. This raises a key question for large-scale training: how much performance is forfeited by these approximations? To probe this question, we establish a practical upper bound on iteration complexity by applying full Gauss-Newton (GN) preconditioning to transformer models of up to 150M parameters. Our experiments show that full GN updates yield substantial gain…

S-D-RSM: Stochastic Distributed Regularized Splitting Method for Large-Scale Convex Optimization Problems
Maoran Wang, Xingju Cai, Yongxin Chen
https://arxiv.org/abs/2511.10133 https://arxiv.org/pdf/2511.10133 https://arxiv.org/html/2511.10133
arXiv:2511.10133v1 Announce Type: new
Abstract: This paper investigates the problems large-scale distributed composite convex optimization, with motivations from a broad range of applications, including multi-agent systems, federated learning, smart grids, wireless sensor networks, compressed sensing, and so on. Stochastic gradient descent (SGD) and its variants are commonly employed to solve such problems. However, existing algorithms often rely on vanishing step sizes, strong convexity assumptions, or entail substantial computational overhead to ensure convergence or obtain favorable complexity. To bridge the gap between theory and practice, we integrate consensus optimization and operator splitting techniques (see Problem Reformulation) to develop a novel stochastic splitting algorithm, termed the \emph{stochastic distributed regularized splitting method} (S-D-RSM). In practice, S-D-RSM performs parallel updates of proximal mappings and gradient information for only a randomly selected subset of agents at each iteration. By introducing regularization terms, it effectively mitigates consensus discrepancies among distributed nodes. In contrast to conventional stochastic methods, our theoretical analysis establishes that S-D-RSM achieves global convergence without requiring diminishing step sizes or strong convexity assumptions. Furthermore, it achieves an iteration complexity of $\mathcal{O}(1/\epsilon)$ with respect to both the objective function value and the consensus error. Numerical experiments show that S-D-RSM achieves up to 2--3$\times$ speedup compared to state-of-the-art baselines, while maintaining comparable or better accuracy. These results not only validate the algorithm's theoretical guarantees but also demonstrate its effectiveness in practical tasks such as compressed sensing and empirical risk minimization.
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MM-LMPC: Multi-Modal Learning Model Predictive Control via Bandit-Based Mode Selection
Wataru Hashimoto, Kazumune Hashimoto
https://arxiv.org/abs/2510.00410 https://

MM-LMPC: Multi-Modal Learning Model Predictive Control via Bandit-Based Mode Selection
Learning Model Predictive Control (LMPC) improves performance on iterative tasks by leveraging data from previous executions. At each iteration, LMPC constructs a sampled safe set from past trajectories and uses it as a terminal constraint, with a terminal cost given by the corresponding cost-to-go. While effective, LMPC heavily depends on the initial trajectories: states with high cost-to-go are rarely selected as terminal candidates in later iterations, leaving parts of the state space unexpl…

Flatness-Aware Stochastic Gradient Langevin Dynamics
Stefano Bruno, Youngsik Hwang, Jaehyeon An, Sotirios Sabanis, Dong-Young Lim
https://arxiv.org/abs/2510.02174 https://

Flatness-Aware Stochastic Gradient Langevin Dynamics
Generalization in deep learning is closely tied to the pursuit of flat minima in the loss landscape, yet classical Stochastic Gradient Langevin Dynamics (SGLD) offers no mechanism to bias its dynamics toward such low-curvature solutions. This work introduces Flatness-Aware Stochastic Gradient Langevin Dynamics (fSGLD), designed to efficiently and provably seek flat minima in high-dimensional nonconvex optimization problems. At each iteration, fSGLD uses the stochastic gradient evaluated at para…

A generalized alternating NGMRES method for PDE-constrained optimization problems governed by transport equations
Yunhui He, Andreas Mang
https://arxiv.org/abs/2510.08782 https:…

A generalized alternating NGMRES method for PDE-constrained optimization problems governed by transport equations
In this work, we propose a generalized alternating nonlinear generalized minimal residual method (GA-NGMRES) to accelerate first-order optimization schemes for PDE-constrained optimization problems governed by transport equations. We apply GA-NGMRES to a preconditioned first-order optimization scheme by interpreting the update rule as a fixed-point (FP) iteration. Our approach introduces a novel periodic mixing strategy that integrates NGMRES updates with FP steps. This new scheme improves effi…

Smoother-type a posteriori error estimates for finite element methods
Yuwen Li, Han Shui
https://arxiv.org/abs/2510.07677 https://arxiv.org/pdf/2510.07677

Smoother-type a posteriori error estimates for finite element methods
This work develops user-friendly a posteriori error estimates of finite element methods, based on smoothers of linear iterative solvers. The proposed method employs simple smoothers, such as Jacobi or Gauss--Seidel iteration, on an auxiliary finer mesh to process the finite element residual for a posteriori error control. The implementation requires only a coarse-to-fine prolongation operator. For symmetric problems, we prove the reliability and efficiency of smoother-type error estimators unde…

On the Benefits of Weight Normalization for Overparameterized Matrix Sensing
Yudong Wei, Liang Zhang, Bingcong Li, Niao He
https://arxiv.org/abs/2510.01175 https://

On the Benefits of Weight Normalization for Overparameterized Matrix Sensing
While normalization techniques are widely used in deep learning, their theoretical understanding remains relatively limited. In this work, we establish the benefits of (generalized) weight normalization (WN) applied to the overparameterized matrix sensing problem. We prove that WN with Riemannian optimization achieves linear convergence, yielding an exponential speedup over standard methods that do not use WN. Our analysis further demonstrates that both iteration and sample complexity improve p…

Accelerated Price Adjustment for Fisher Markets with Exact Recovery of Competitive Equilibrium
He Chen, Chonghe Jiang, Anthony Man-Cho So
https://arxiv.org/abs/2510.07759 https:…

Accelerated Price Adjustment for Fisher Markets with Exact Recovery of Competitive Equilibrium
The canonical price-adjustment process, tâtonnement, typically fails to converge to the exact competitive equilibrium (CE) and requires a high iteration complexity of $\tilde{\mathcal{O}}(1/ε)$ to compute $ε$-CE prices in widely studied linear and quasi-linear Fisher markets. This paper proposes refined price-adjustment processes to overcome these limitations. By formulating the task of finding CE of a (quasi-)linear Fisher market as a strongly convex nonsmooth minimization problem, we devel…

On the Complexity of Lower-Order Implementations of Higher-Order Methods
Nikita Doikov, Geovani Nunes Grapiglia
https://arxiv.org/abs/2510.07992 https://ar…

On the Complexity of Lower-Order Implementations of Higher-Order Methods
In this work, we propose a method for minimizing non-convex functions with Lipschitz continuous $p$th-order derivatives, starting from $p \geq 1$. The method, however, only requires derivative information up to order $(p-1)$, since the $p$th-order derivatives are approximated via finite differences. To ensure oracle efficiency, instead of computing finite-difference approximations at every iteration, we reuse each approximation for $m$ consecutive iterations before recomputing it, with $m \geq …

Mixed-precision iterative refinement for low-rank Lyapunov equations
Peter Benner, Xiaobo Liu
https://arxiv.org/abs/2510.02126 https://arxiv.org/pdf/2510.0…

Mixed-precision iterative refinement for low-rank Lyapunov equations
We develop a mixed-precision iterative refinement framework for solving low-rank Lyapunov matrix equations $AX + XA^T + W =0$, where $W=LL^T$ or $W=LSL^T$. Via rounding error analysis of the algorithms we derive sufficient conditions for the attainable normwise residuals in different precision settings and show how the algorithmic parameters should be chosen. Using the sign function Newton iteration as the solver, we show that reduced precisions, such as the half precision, can be used as the s…

dHPR: A Distributed Halpern Peaceman--Rachford Method for Non-smooth Distributed Optimization Problems
Zhangcheng Feng, Defeng Sun, Yancheng Yuan, Guojun Zhang
https://arxiv.org/abs/2511.10069 https://arxiv.org/pdf/2511.10069 https://arxiv.org/html/2511.10069
arXiv:2511.10069v1 Announce Type: new
Abstract: This paper introduces the distributed Halpern Peaceman--Rachford (dHPR) method, an efficient algorithm for solving distributed convex composite optimization problems with non-smooth objectives, which achieves a non-ergodic $O(1/k)$ iteration complexity regarding Karush--Kuhn--Tucker residual. By leveraging the symmetric Gauss--Seidel decomposition, the dHPR effectively decouples the linear operators in the objective functions and consensus constraints while maintaining parallelizability and avoiding additional large proximal terms, leading to a decentralized implementation with provably fast convergence. The superior performance of dHPR is demonstrated through comprehensive numerical experiments on distributed LASSO, group LASSO, and $L_1$-regularized logistic regression problems.
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An inexact semismooth Newton-Krylov method for semilinear elliptic optimal control problem
Shiqi Chen, Xuesong Chen
https://arxiv.org/abs/2511.10058 https://arxiv.org/pdf/2511.10058 https://arxiv.org/html/2511.10058
arXiv:2511.10058v1 Announce Type: new
Abstract: An inexact semismooth Newton method has been proposed for solving semi-linear elliptic optimal control problems in this paper. This method incorporates the generalized minimal residual (GMRES) method, a type of Krylov subspace method, to solve the Newton equations and utilizes nonmonotonic line search to adjust the iteration step size. The original problem is reformulated into a nonlinear equation through variational inequality principles and discretized using a second-order finite difference scheme. By leveraging slanting differentiability, the algorithm constructs semismooth Newton directions and employs GMRES method to inexactly solve the Newton equations, significantly reducing computational overhead. A dynamic nonmonotonic line search strategy is introduced to adjust stepsizes adaptively, ensuring global convergence while overcoming local stagnation. Theoretical analysis demonstrates that the algorithm achieves superlinear convergence near optimal solutions when the residual control parameter $\eta_k$ approaches to 0. Numerical experiments validate the method's accuracy and efficiency in solving semilinear elliptic optimal control problems, corroborating theoretical insights.
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A Computationally Efficient Finite Element Method for Shape Reconstruction of Inverse Conductivity Problems
Lefu Cai, Zhixin Liu, Minghui Song, Xianchao Wang
https://arxiv.org/abs/2510.00597

A Computationally Efficient Finite Element Method for Shape Reconstruction of Inverse Conductivity Problems
The inverse conductivity problem aims at determining the unknown conductivity inside a bounded domain from boundary measurements. In practical applications, algorithms based on minimizing a regularized residual functional subject to PDE constraints have been widely used to deal with this problem. However, such approaches typically require repeated iterations and solving the forward problem at each iteration, which leads to a heavy computational cost. To address this issue, we first reformulate …

(Adaptive) Scaled gradient methods beyond locally Holder smoothness: Lyapunov analysis, convergence rate and complexity
Susan Ghaderi, Morteza Rahimi, Yves Moreau, Masoud Ahookhosh
https://arxiv.org/abs/2511.10425 https://arxiv.org/pdf/2511.10425 https://arxiv.org/html/2511.10425
arXiv:2511.10425v1 Announce Type: new
Abstract: This paper addresses the unconstrained minimization of smooth convex functions whose gradients are locally Holder continuous. Building on these results, we analyze the Scaled Gradient Algorithm (SGA) under local smoothness assumptions, proving its global convergence and iteration complexity. Furthermore, under local strong convexity and the Kurdyka-Lojasiewicz (KL) inequality, we establish linear convergence rates and provide explicit complexity bounds. In particular, we show that when the gradient is locally Lipschitz continuous, SGA attains linear convergence for any KL exponent. We then introduce and analyze an adaptive variant of SGA (AdaSGA), which automatically adjusts the scaling and step-size parameters. For this method, we show global convergence, and derive local linear rates under strong convexity.
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Measuring dissimilarity between convex cones by means of max-min angles
Welington de Oliveira, Valentina Sessa, David Sossa
https://arxiv.org/abs/2511.10483 https://arxiv.org/pdf/2511.10483 https://arxiv.org/html/2511.10483
arXiv:2511.10483v1 Announce Type: new
Abstract: This work introduces a novel dissimilarity measure between two convex cones, based on the max-min angle between them. We demonstrate that this measure is closely related to the Pompeiu-Hausdorff distance, a well-established metric for comparing compact sets. Furthermore, we examine cone configurations where the measure admits simplified or analytic forms. For the specific case of polyhedral cones, a nonconvex cutting-plane method is deployed to compute, at least approximately, the measure between them. Our approach builds on a tailored version of Kelley's cutting-plane algorithm, which involves solving a challenging master program per iteration. When this master program is solved locally, our method yields an angle that satisfies certain necessary optimality conditions of the underlying nonconvex optimization problem yielding the dissimilarity measure between the cones. As an application of the proposed mathematical and algorithmic framework, we address the image-set classification task under limited data conditions, a task that falls within the scope of the \emph{Few-Shot Learning} paradigm. In this context, image sets belonging to the same class are modeled as polyhedral cones, and our dissimilarity measure proves useful for understanding whether two image sets belong to the same class.
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A Time-certified Predictor-corrector IPM Algorithm for Box-QP
Liang Wu, Yunhong Che, Richard D. Braatz, Jan Drgona
https://arxiv.org/abs/2510.04467 https://

A Time-certified Predictor-corrector IPM Algorithm for Box-QP
Minimizing both the worst-case and average execution times of optimization algorithms is equally critical in real-time optimization-based control applications such as model predictive control (MPC). Most MPC solvers have to trade off between certified worst-case and practical average execution times. For example, our previous work [1] proposed a full-Newton path-following interior-point method (IPM) with data-independent, simple-calculated, and exact $O(\sqrt{n})$ iteration complexity, but not …

Exponential convergence of a distributed divide-and-conquer algorithm for constrained convex optimization on networks
Nazar Emirov, Guohui Song, Qiyu Sun
https://arxiv.org/abs/2510.01511

Exponential convergence of a distributed divide-and-conquer algorithm for constrained convex optimization on networks
We propose a divide-and-conquer (DAC) algorithm for constrained convex optimization over networks, where the global objective is the sum of local objectives attached to individual agents. The algorithm is fully distributed: each iteration solves local subproblems around selected fusion centers and coordinates only with neighboring fusion centers. Under standard assumptions of smoothness, strong convexity, and locality on the objective function, together with polynomial growth conditions on the …

DeMuon: A Decentralized Muon for Matrix Optimization over Graphs
Chuan He, Shuyi Ren, Jingwei Mao, Erik G. Larsson
https://arxiv.org/abs/2510.01377 https://

DeMuon: A Decentralized Muon for Matrix Optimization over Graphs
In this paper, we propose DeMuon, a method for decentralized matrix optimization over a given communication topology. DeMuon incorporates matrix orthogonalization via Newton-Schulz iterations-a technique inherited from its centralized predecessor, Muon-and employs gradient tracking to mitigate heterogeneity among local functions. Under heavy-tailed noise conditions and additional mild assumptions, we establish the iteration complexity of DeMuon for reaching an approximate stochastic stationary …