Tootfinder

Second-order Optimization under Heavy-Tailed Noise: Hessian Clipping and Sample Complexity Limits
Abdurakhmon Sadiev, Peter Richt\'arik, Ilyas Fatkhullin
https://arxiv.org/abs/2510.10690

Second-order Optimization under Heavy-Tailed Noise: Hessian Clipping and Sample Complexity Limits
Heavy-tailed noise is pervasive in modern machine learning applications, arising from data heterogeneity, outliers, and non-stationary stochastic environments. While second-order methods can significantly accelerate convergence in light-tailed or bounded-noise settings, such algorithms are often brittle and lack guarantees under heavy-tailed noise -- precisely the regimes where robustness is most critical. In this work, we take a first step toward a theoretical understanding of second-order opt…

Affine-Orthogonal Manifolds and Deformation to Levi-Civita Connections
Mihail Cocos
https://arxiv.org/abs/2510.09648 https://arxiv.org/pdf/2510.09648

Affine-Orthogonal Manifolds and Deformation to Levi-Civita Connections
We study a class of affine manifolds equipped with a flat affine connection $\nabla$ and a global Riemannian metric $g$ that is diagonal in local affine coordinates. These structures are closely related to \emph{Hessian manifolds}, where the metric locally arises as the Hessian of a smooth potential. For example, the Hopf manifold $(\mathbb{R}^{n+1}\setminus \{0\}) / \langle x \mapsto 2x \rangle$ with metric $g = (\sum_i x_i^2)^{-1} \sum_i dx_i^2$ admits a proper deformation of $\nabla$ into it…

Contraction and entropy production in continuous-time Sinkhorn dynamics
Anand Srinivasan, Jean-Jacques Slotine
https://arxiv.org/abs/2510.12639 https://arx…

Contraction and entropy production in continuous-time Sinkhorn dynamics
Recently, the vanishing-step-size limit of the Sinkhorn algorithm at finite regularization parameter $\varepsilon$ was shown to be a mirror descent in the space of probability measures. We give $L^2$ contraction criteria in two time-dependent metrics induced by the mirror Hessian, which reduce to the coercivity of certain conditional expectation operators. We then give an exact identity for the entropy production rate of the Sinkhorn flow, which was previously known only to be nonpositive. Exam…

An inverse problem for the Monge-Amp\`ere equation
Tony Liimatainen, Yi-Hsuan Lin
https://arxiv.org/abs/2510.11572 https://arxiv.org/pdf/2510.11572

An inverse problem for the Monge-Ampère equation
We extend the study of inverse boundary value problems to the setting of fully nonlinear PDEs by considering an inverse source problem for the Monge-Ampère equation \[ \det D^2 u = F. \] We prove that, on a convex Euclidean domain in the plane, the associated Dirichlet-to-Neumann (DN) map uniquely determines a positive source function $F$. The proof relies on recovering the Hessian of a solution to the equation, which is interpreted as a Riemannian metric $g$. Interestingly, although t…

NeST-BO: Fast Local Bayesian Optimization via Newton-Step Targeting of Gradient and Hessian Information
Wei-Ting Tang, Akshay Kudva, Joel A. Paulson
https://arxiv.org/abs/2510.05516

NeST-BO: Fast Local Bayesian Optimization via Newton-Step Targeting of Gradient and Hessian Information
Bayesian optimization (BO) is effective for expensive black-box problems but remains challenging in high dimensions. We propose NeST-BO, a local BO method that targets the Newton step by jointly learning gradient and Hessian information with Gaussian process surrogates, and selecting evaluations via a one-step lookahead bound on Newton-step error. We show that this bound (and hence the step error) contracts with batch size, so NeST-BO directly inherits inexact-Newton convergence: global progres…

Symmetric Persistent Tensors and their Hessian
Masoud Gharahi, Giorgio Ottaviani
https://arxiv.org/abs/2510.07404 https://arxiv.org/pdf/2510.07404

Symmetric Persistent Tensors and their Hessian
Persistent tensors, introduced in [Quantum 8 (2024), 1238], and inspired by quantum information theory, form a recursively defined class of tensors that remain stable under the substitution method and thereby yield nontrivial lower bounds on tensor rank. In this work, we investigate the symmetric case-namely, symmetric persistent tensors, or equivalently, persistent polynomials. We establish that a symmetric tensor in $\mathrm{Sym}^n \mathbb{C}^d$ is persistent if the determinant of its Hessian…

Replaced article(s) found for math.OC. https://arxiv.org/list/math.OC/new
[1/1]:
- A robust BFGS algorithm for unconstrained nonlinear optimization problems
Yaguang Yang
https://arxiv.org/abs/1212.5929
- Quantum computing and the stable set problem
Alja\v{z} Krpan, Janez Povh, Dunja Pucher
https://arxiv.org/abs/2405.12845 https://mastoxiv.page/@arXiv_mathOC_bot/112483516437815686
- Mean Field Game with Reflected Jump Diffusion Dynamics: A Linear Programming Approach
Zongxia Liang, Xiang Yu, Keyu Zhang
https://arxiv.org/abs/2508.20388 https://mastoxiv.page/@arXiv_mathOC_bot/115111048711698998
- Differential Dynamic Programming for the Optimal Control Problem with an Ellipsoidal Target Set a...
Sungjun Eom, Gyunghoon Park
https://arxiv.org/abs/2509.07546 https://mastoxiv.page/@arXiv_mathOC_bot/115179281556444440
- On the Moreau envelope properties of weakly convex functions
Marien Renaud, Arthur Leclaire, Nicolas Papadakis
https://arxiv.org/abs/2509.13960 https://mastoxiv.page/@arXiv_mathOC_bot/115224514482363803
- Automated algorithm design via Nevanlinna-Pick interpolation
Ibrahim K. Ozaslan, Tryphon T. Georgiou, Mihailo R. Jovanovic
https://arxiv.org/abs/2509.21416 https://mastoxiv.page/@arXiv_mathOC_bot/115286533597711930
- Optimal Control of a Bioeconomic Crop-Energy System with Energy Reinvestment
Othman Cherkaoui Dekkaki
https://arxiv.org/abs/2510.11381 https://mastoxiv.page/@arXiv_mathOC_bot/115372322896073250
- Point Convergence Analysis of the Accelerated Gradient Method for Multiobjective Optimization: Co...
Yingdong Yin
https://arxiv.org/abs/2510.26382 https://mastoxiv.page/@arXiv_mathOC_bot/115468018035252078
- History-Aware Adaptive High-Order Tensor Regularization
Chang He, Bo Jiang, Yuntian Jiang, Chuwen Zhang, Shuzhong Zhang
https://arxiv.org/abs/2511.05788
- Equivalence of entropy solutions and gradient flows for pressureless 1D Euler systems
Jos\'e Antonio Carrillo, Sondre Tesdal Galtung
https://arxiv.org/abs/2312.04932 https://mastoxiv.page/@arXiv_mathAP_bot/111560077272113052
- Kernel Modelling of Fading Memory Systems
Yongkang Huo, Thomas Chaffey, Rodolphe Sepulchre
https://arxiv.org/abs/2403.11945 https://mastoxiv.page/@arXiv_eessSY_bot/112121123836064435
- The Maximum Theoretical Ground Speed of the Wheeled Vehicle
Altay Zhakatayev, Mukatai Nemerebayev
https://arxiv.org/abs/2502.15341 https://mastoxiv.page/@arXiv_physicsclassph_bot/114057765769441123
- Hessian stability and convergence rates for entropic and Sinkhorn potentials via semiconcavity
Giacomo Greco, Luca Tamanini
https://arxiv.org/abs/2504.11133 https://mastoxiv.page/@arXiv_mathPR_bot/114346453424694503
- Optimizing the ground state energy of the three-dimensional magnetic Dirichlet Laplacian with con...
Matthias Baur
https://arxiv.org/abs/2504.21597 https://mastoxiv.page/@arXiv_mathph_bot/114431404740241516
- A localized consensus-based sampling algorithm
Arne Bouillon, Alexander Bodard, Panagiotis Patrinos, Dirk Nuyens, Giovanni Samaey
https://arxiv.org/abs/2505.24861 https://mastoxiv.page/@arXiv_mathNA_bot/114612580684567066
- A Novel Sliced Fused Gromov-Wasserstein Distance
Moritz Piening, Robert Beinert
https://arxiv.org/abs/2508.02364 https://mastoxiv.page/@arXiv_csLG_bot/114976243138728278
- Minimal Regret Walras Equilibria for Combinatorial Markets via Duality, Integrality, and Sensitiv...
Alo\"is Duguet, Tobias Harks, Martin Schmidt, Julian Schwarz
https://arxiv.org/abs/2511.09021 https://mastoxiv.page/@arXiv_csGT_bot/115541243299714775
toXiv_bot_toot

Bayesian Influence Functions for Hessian-Free Data Attribution
Philipp Alexander Kreer, Wilson Wu, Maxwell Adam, Zach Furman, Jesse Hoogland
https://arxiv.org/abs/2509.26544 htt…

Bayesian Influence Functions for Hessian-Free Data Attribution
Classical influence functions face significant challenges when applied to deep neural networks, primarily due to non-invertible Hessians and high-dimensional parameter spaces. We propose the local Bayesian influence function (BIF), an extension of classical influence functions that replaces Hessian inversion with loss landscape statistics that can be estimated via stochastic-gradient MCMC sampling. This Hessian-free approach captures higher-order interactions among parameters and scales efficie…

Crosslisted article(s) found for math.AC. https://arxiv.org/list/math.AC/new
[1/1]:
- Symmetric Persistent Tensors and their Hessian
Masoud Gharahi, Giorgio Ottaviani

Deformation quantization of a hessian KV- structure on $\mathbb{R}^2$
Herguey Mopeng, Prosper Rosaire Mama Assandje, Joseph Dongho, Armand Tsimi
https://arxiv.org/abs/2509.23228

Deformation quantization of a hessian KV- structure on $\mathbb{R}^2$
This paper studies the quantization of the deformation of Hessian structures on a two-dimensional vector space, in the framework of Koszul-Vinberg algebras. We analyze how Hessian structures can be deformed to obtain quantum structures while preserving certain geometric and algebraic properties. The aim of the paper is to establish links between deformation theory and Hessian geometry.

Re$^3$MCN: Cubic Newton Variance Reduction Momentum Quadratic Regularization for Finite-sum Non-convex Problems
Dmitry Pasechnyuk-Vilensky, Dmitry Kamzolov, Martin Tak\'a\v{c}
https://arxiv.org/abs/2510.08714

Re$^3$MCN: Cubic Newton + Variance Reduction + Momentum + Quadratic Regularization for Finite-sum Non-convex Problems
We analyze a stochastic cubic regularized Newton method for finite sum optimization $\textstyle\min_{x\in\mathbb{R}^d} F(x) \;=\; \frac{1}{n}\sum_{i=1}^n f_i(x)$, that uses SARAH-type recursive variance reduction with mini-batches of size $b\sim n^{1/2}$ and exponential moving averages (EMA) for gradient and Hessian estimators. We show that the method achieves a $(\varepsilon,\sqrt{L_2\varepsilon})$-second-order stationary point (SOSP) with total stochastic oracle calls $n + \widetilde{\mathcal…

Colibri: A new tool for fast-flying PDF fits
Mark N. Costantini, Luca Mantani, James M. Moore, Valentina Schutze Sanchez, Maria Ubiali
https://arxiv.org/abs/2510.03391 https://

Colibri: A new tool for fast-flying PDF fits
We present Colibri, an open-source Python code that provides a general and flexible tool for PDF fits. The code is built so that users can implement their own PDF model, and use the built-in functionalities of Colibri for a fast computation of observables. It grants easy access to experimental data, several error propagation methodologies, including the Hessian method, the Monte Carlo replica method, and an efficient numerical Bayesian sampling algorithm. To demonstrate the capabilities of Coli…

Quantum Fisher information matrices from R\'enyi relative entropies
Mark M. Wilde
https://arxiv.org/abs/2510.02218 https://arxiv.org/pdf/2510.02218

Quantum Fisher information matrices from Rényi relative entropies
Quantum generalizations of the Fisher information are important in quantum information science, with applications in high energy and condensed matter physics and in quantum estimation theory, machine learning, and optimization. One can derive a quantum generalization of the Fisher information matrix in a natural way as the Hessian matrix arising in a Taylor expansion of a smooth divergence. Such an approach is appealing for quantum information theorists, given the ubiquity of divergences in qua…

Scalable Hessian-free Proximal Conjugate Gradient Method for Nonconvex and Nonsmooth Optimization
Yiming Zhou, Wei Dai
https://arxiv.org/abs/2509.15973 https://

Scalable Hessian-free Proximal Conjugate Gradient Method for Nonconvex and Nonsmooth Optimization
This work studies a composite minimization problem involving a differentiable function q and a nonsmooth function h, both of which may be nonconvex. This problem is ubiquitous in signal processing and machine learning yet remains challenging to solve efficiently, particularly when large-scale instances, poor conditioning, and nonconvexity coincide. To address these challenges, we propose a proximal conjugate gradient method (PCG) that matches the fast convergence of proximal (quasi-)Newton algo…

A special concavity property for positive Hessian quotient operators
Pengfei Guan, Marcin Sroka
https://arxiv.org/abs/2509.16406 https://arxiv.org/pdf/2509…

A special concavity property for positive Hessian quotient operators
We establish a special concavity property for positive Hessian quotient operators $\frac{σ_n(W)}{σ_{n-k}(W)}, \ 1\le k\le n-1$. As a consequence, we prove a Jacobi inequality for general symmetric tensor satisfying positive Hessian quotient equation on Riemannian manifolds.

Several sufficient conditions for projective hypersurfaces to be GIT (semi)stable
Xuancong He
https://arxiv.org/abs/2510.03695 https://arxiv.org/pdf/2510.0…

Several sufficient conditions for projective hypersurfaces to be GIT (semi)stable
In this paper, I present some sufficient conditions for projective hypersurfaces to be GIT (semi-)stable. These conditions will be presented in terms of dimension and degree of the hypersurfaces, dimension of the singular locus and multiplicities of the singular points. When singularities of the hypersurface are isolated and all have multiplicity 2, we can judge its stability via the ranks of Hessian matrices at these singular points.

Optimal Zeroth-Order Bilevel Optimization
Alireza Aghasi, Jeongyeol Kwon, Saeed Ghadimi
https://arxiv.org/abs/2510.03646 https://arxiv.org/pdf/2510.03646…

Optimal Zeroth-Order Bilevel Optimization
In this paper, we develop zeroth-order algorithms with provably (nearly) optimal sample complexity for stochastic bilevel optimization, where only noisy function evaluations are available. We propose two distinct algorithms: the first is inspired by Jacobian/Hessian-based approaches, and the second builds on using a penalty function reformulation. The Jacobian/Hessian-based method achieves a sample complexity of $\mathcal{O}(d^3/ε^2)$, which is optimal in terms of accuracy $ε$, albeit with po…

Finite Element Complexes with Traces Structures: A unified framework for cohomology and bounded interpolation
Jun Hu, Yizhou Liang, Ting Lin
https://arxiv.org/abs/2509.23788 htt…

Finite Element Complexes with Traces Structures: A unified framework for cohomology and bounded interpolation
This paper considers the cohomology and bounded interpolation of nonstandard finite element complexes, e.g. Stokes, Hessian, Elasticity, divdiv. Compared to the standard finite element exterior calculus, the main challenge is the existence of extra smoothness. This paper provides a unified framework for finite element complexes with extra smoothness. The trace structure is introduced to derive the bubble complexes in different dimensions (vertices, edges, faces). It is shown that if the bubble …

The Rabinowitz minimal periodic solution conjecture on partially convex reversible Hamiltonian systems and brake subharmonics
Yuting Zhou
https://arxiv.org/abs/2509.25567 https:…

The Rabinowitz minimal periodic solution conjecture on partially convex reversible Hamiltonian systems and brake subharmonics
Under weaker regularity and compactness assumptions, we find the mountain-pass essential point, which is a novel extension of the classical Ambrosetti-Rabinowitz mountain pass theorem. We study the reversible superquadratic autonomous Hamiltonian systems whose Hamiltonian $H(p,q)$ is strictly convex in the position $q\in\mathbf{R}^n$ and prove that for every $T>0$, the system has a $T$-periodic brake solution $\bar x$ with minimal period $T$, provided the Hessian $H_{pp}(\bar x(t))\in\mathbf{R}…

Some shape functionals for the $k$-Hessian equation
Alba Lia Masiello, Francesco Salerno
https://arxiv.org/abs/2509.21313 https://arxiv.org/pdf/2509.21313

Some shape functionals for the $k$-Hessian equation
For a non-empty, bounded, open, and convex set of class $C^2$, we consider the Torsional Rigidity associated to the $k$-Hessian operator. We first prove Pólya type lower bound for the $k$-Torsional Rigidity in any dimension; then, in order to investigate optimal sets in the Pólya type inequality, we provide two quantitative estimates.

Sharpness of Minima in Deep Matrix Factorization: Exact Expressions
Anil Kamber, Rahul Parhi
https://arxiv.org/abs/2509.25783 https://arxiv.org/pdf/2509.25…

Sharpness of Minima in Deep Matrix Factorization: Exact Expressions
Understanding the geometry of the loss landscape near a minimum is key to explaining the implicit bias of gradient-based methods in non-convex optimization problems such as deep neural network training and deep matrix factorization. A central quantity to characterize this geometry is the maximum eigenvalue of the Hessian of the loss, which measures the sharpness of the landscape. Currently, its precise role has been obfuscated because no exact expressions for this sharpness measure were known i…

On the non-existence of certain real algebraic surfaces
Miguel Angel Guadarrama-Garc\'ia
https://arxiv.org/abs/2510.04025 https://arxiv.org/pdf/2510.04…

On the non-existence of certain real algebraic surfaces
In this note is given an algebraic solution to the problem 1997-6 proposed by D. A. Panov in the list of Arnold's problems \cite{Arnld2b}. In particular, it is shown that there does not exist a real polynomial function $f$ on the real euclidean plane, whose Hessian is positive in an open set bordered by smooth connected curve, and the parabolic curve of the graph of $f$ has only one special parabolic point with index $+1$. Besides, we find conditions on $f$ so that its graph has more special pa…

Constrained Dikin-Langevin diffusion for polyhedra
James Chok, Domenic Petzinna
https://arxiv.org/abs/2510.04582 https://arxiv.org/pdf/2510.04582

Constrained Dikin-Langevin diffusion for polyhedra
Interior-point geometry offers a straightforward approach to constrained sampling and optimization on polyhedra, eliminating reflections and ad hoc projections. We exploit the Dikin log-barrier to define a Dikin--Langevin diffusion whose drift and noise are modulated by the inverse barrier Hessian. In continuous time, we establish a boundary no-flux property; trajectories started in the interior remain in $U$ almost surely, so feasibility is maintained by construction. For computation, we adopt…

Inexact and Stochastic Gradient Optimization Algorithms with Inertia and Hessian Driven Damping
Harsh Choudhary, Jalal Fadili, Vyachelav Kungurtsev
https://arxiv.org/abs/2509.19561

Inexact and Stochastic Gradient Optimization Algorithms with Inertia and Hessian Driven Damping
In a real Hilbert space setting, we study the convergence properties of an inexact gradient algorithm featuring both viscous and Hessian driven damping for convex differentiable optimization. In this algorithm, the gradient evaluation can be subject to deterministic and stochastic perturbations. In the deterministic case, we show that under appropriate summability assumptions on the perturbation, our algorithm enjoys fast convergence of the objective values, of the gradients and weak convergenc…

Replaced article(s) found for hep-lat. https://arxiv.org/list/hep-lat/new
[1/1]:
- Gradient and Hessian-Based Temperature Estimator in Lattice Gauge Theories: A Diagnostic Tool for...
Navdeep Singh Dhindsa, Anosh Joseph, Vamika Longia

XQC: Well-conditioned Optimization Accelerates Deep Reinforcement Learning
Daniel Palenicek, Florian Vogt, Joe Watson, Ingmar Posner, Jan Peters
https://arxiv.org/abs/2509.25174

XQC: Well-conditioned Optimization Accelerates Deep Reinforcement Learning
Sample efficiency is a central property of effective deep reinforcement learning algorithms. Recent work has improved this through added complexity, such as larger models, exotic network architectures, and more complex algorithms, which are typically motivated purely by empirical performance. We take a more principled approach by focusing on the optimization landscape of the critic network. Using the eigenspectrum and condition number of the critic's Hessian, we systematically investigate the i…

Haussdorff consistency of MLE in folded normal and Gaussian mixtures
Koustav Mallik
https://arxiv.org/abs/2509.12206 https://arxiv.org/pdf/2509.12206

Haussdorff consistency of MLE in folded normal and Gaussian mixtures
We develop a constant-tracking likelihood theory for two nonregular models: the folded normal and finite Gaussian mixtures. For the folded normal, we prove boundary coercivity for the profiled likelihood, show that the profile path of the location parameter exists and is strictly decreasing by an implicit-function argument, and establish a unique profile maximizer in the scale parameter. Deterministic envelopes for the log-likelihood, the score, and the Hessian yield elementary uniform laws of …

Introduction to Interpolation-Based Optimization
Lindon Roberts
https://arxiv.org/abs/2510.04473 https://arxiv.org/pdf/2510.04473

Introduction to Interpolation-Based Optimization
The field of derivative-free optimization (DFO) studies algorithms for nonlinear optimization that do not rely on the availability of gradient or Hessian information. It is primarily designed for settings when functions are black-box, expensive to evaluate and/or noisy. A widely used and studied class of DFO methods for local optimization is interpolation-based optimization (IBO), also called model-based DFO, where the general principles from derivative-based nonlinear optimization algorithms a…

A Sequential Quadratic Programming Perspective on Optimal Control
Abhijeet, Suman Chakravorty
https://arxiv.org/abs/2510.03475 https://arxiv.org/pdf/2510.0…

A Sequential Quadratic Programming Perspective on Optimal Control
This paper offers a unified perspective on different approaches to the solution of optimal control problems through the lens of constrained sequential quadratic programming. In particular, it allows us to find the relationships between Newton's method, the iterative LQR (iLQR), and Differential Dynamic Programming (DDP) approaches to solve the problem. It is shown that the iLQR is a principled SQP approach, rather than simply an approximation of DDP by neglecting the Hessian terms, to solve opt…

Hessian-guided Perturbed Wasserstein Gradient Flows for Escaping Saddle Points
Naoya Yamamoto, Juno Kim, Taiji Suzuki
https://arxiv.org/abs/2509.16974 https://

Hessian-guided Perturbed Wasserstein Gradient Flows for Escaping Saddle Points
Wasserstein gradient flow (WGF) is a common method to perform optimization over the space of probability measures. While WGF is guaranteed to converge to a first-order stationary point, for nonconvex functionals the converged solution does not necessarily satisfy the second-order optimality condition; i.e., it could converge to a saddle point. In this work, we propose a new algorithm for probability measure optimization, perturbed Wasserstein gradient flow (PWGF), that achieves second-order opt…

Improving Online-to-Nonconvex Conversion for Smooth Optimization via Double Optimism
Francisco Patitucci, Ruichen Jiang, Aryan Mokhtari
https://arxiv.org/abs/2510.03167 https://…

Improving Online-to-Nonconvex Conversion for Smooth Optimization via Double Optimism
A recent breakthrough in nonconvex optimization is the online-to-nonconvex conversion framework of \cite{cutkosky2023optimal}, which reformulates the task of finding an $\varepsilon$-first-order stationary point as an online learning problem. When both the gradient and the Hessian are Lipschitz continuous, instantiating this framework with two different online learners achieves a complexity of $\mathcal{O}(\varepsilon^{-1.75}\log(1/\varepsilon))$ in the deterministic case and a complexity of $\…

Crosslisted article(s) found for math.DG. https://arxiv.org/list/math.DG/new
[1/1]:
- A special concavity property for positive Hessian quotient operators
Pengfei Guan, Marcin Sroka

Convergence rates for the vanishing viscosity approximation of fully nonlinear, non-convex, second-order Hamilton-Jacobi equations
Alekos Cecchin, Alessandro Goffi
https://arxiv.org/abs/2509.12144

Convergence rates for the vanishing viscosity approximation of fully nonlinear, non-convex, second-order Hamilton-Jacobi equations
We obtain new quantitative estimates of the vanishing viscosity approximation for time-dependent, degenerate, Hamilton-Jacobi equations that are neither concave nor convex in the gradient and Hessian entries of the form $\partial_t u+H(x,t,Du,D^2u)=0$ in the whole space. We approximate the PDE with a fully nonlinear, possibly degenerate, elliptic operator $\varepsilon F(x,t,D^2u)$. Assuming that $u\in C^α_x$, $u_0\in C^η$, $H\in C^β_x$ and having power growth $γ$ in the gradient entry, we e…

Regularized Overestimated Newton
Danny Duan, Hanbaek Lyu
https://arxiv.org/abs/2509.21684 https://arxiv.org/pdf/2509.21684…

Regularized Overestimated Newton
We propose Regularized Overestimated Newton (RON), a Newton-type method with low per-iteration cost and strong global and local convergence guarantees for smooth convex optimization. RON interpolates between gradient descent and globally regularized Newton, with behavior determined by the largest Hessian overestimation error. Globally, when the optimality gap of the objective is large, RON achieves an accelerated $O(n^{-2})$ convergence rate; when small, its rate becomes $O(n^{-1})$. Locally, R…