#convergence analysis
27 papers match
The Convergence Behavior of Adam under Heavy-Tailed Noise
Yijiang Pang
The paper provides the first convergence guarantees for the standard vector-form Adam optimizer under heavy‑tailed stochastic noise, showing convergence to stationary points with s…
A new theorem of alternatives leading to sufficient conditions for the superiorization guarantee question of Dynamic String-Averaging in the inconsistent case
Kay Barshad, Yair Censor
The paper introduces a new theorem of alternatives for the Superiorization Methodology applied to General Dynamic String-Averaging in inconsistent feasibility problems, providing s…
Adaptive Gradient-Based Methods for a Broader Class of Optimization Problems under Performative Prediction
Hiroki Hamaguchi, Yuya Hikima, Hiroshi Sawada +1
The paper proposes a gradient-based optimization algorithm that estimates distribution shifts via finite differences, providing convergence guarantees for a wider range of loss fun…
Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws
Hendrik Ranocha
The paper extends convergence analysis for entropy-conservative summation-by-parts (SBP) discretizations to general hyperbolic systems with convex entropy and source terms, and to…
Optimization under Persistent State-Dependent Bias: Gradient-based Method and Complexity Analysis
Zhaoxian Wu, Quan Xiao, Tayfun Gokmen +1
The paper analyzes how stochastic gradient descent behaves when updates are consistently distorted by state-dependent scaling, shows this leads to a biased solution, and introduces…
Proximal Gradient Methods for Unconstrained Set Optimization Problems with Set-Valued Maps of Finite Cardinality
Ravi Raushan, Debdas Ghosh, Anshika +1
The paper proposes two proximal gradient algorithms (with and without an Armijo‑type line search) for unconstrained set‑valued optimization problems with finitely many component fu…
Inertial Primal Dual Dynamics with Hessian-driven Damping for Saddle Point Problems
Zepeng Wang, Juan Peypouquet
The paper introduces two inertial primal‑dual dynamical systems with Hessian‑driven damping to solve smooth saddle‑point problems, proving fast convergence rates for both convex‑co…
A low-rank hierarchical framework for the non-Markovian stochastic Schrödinger equation with convergence analysis
Zhuohan Zhang, Zhenning Cai
The paper introduces a low‑rank hierarchical numerical method for solving the non‑Markovian stochastic Schrödinger equation, provides a rigorous convergence analysis, and shows tha…
Fully discrete least-squares splitting scheme for the Monge-Ampère equation: finite element analysis and convergence
Anna Peruso
The paper introduces a fully discrete finite element framework for the two‑dimensional Dirichlet Monge‑Ampère equation using a least‑squares splitting algorithm, and provides conve…
Full Convergence of Regularized Methods for Unconstrained Optimization
Andrea Cristofari
The paper shows that unconstrained optimization algorithms using locally quadratic models regularized by a high‑order norm term generate a fully convergent sequence of iterates for…
Bridging the Gap between Newton-Raphson Method and Regularized Policy Iteration
Zeyang Li, Chuxiong Hu, Yunan Wang +4
The paper shows that regularized policy iteration in reinforcement learning is mathematically equivalent to applying the Newton‑Raphson method to a smoothed Bellman equation, provi…
What's in a Smoothness Constant? Tighter Rates for Local SGD with Bounded Second-order Heterogeneity
Kumar Kshitij Patel, Rustem Islamov, Sebastian U Stich +3
The paper establishes tighter convergence rates for Local SGD (Federated Averaging) on general convex problems under a bounded second‑order heterogeneity assumption, and provides n…
Convergence of the Markovian Iteration for Coupled FBSDEs via a Differentiation Approach
Zhipeng Huang, Cornelis W. Oosterlee
The paper presents a new differentiation-based technique to ensure convergence of a Markovian iteration method for solving fully coupled forward-backward stochastic differential eq…
Convergence Rates for Distribution Matching with Sliced Optimal Transport
Gauthier Thurin, Claire Boyer, Kimia Nadjahi
The paper analyzes an iterative sliced optimal transport method for matching probability distributions, providing non‑asymptotic convergence rates and showing how the method behave…
Approximation of solutions of parameter-dependent problems by residual neural networks
Ana Carpio
The paper introduces a simple training scheme for residual neural networks based on analytic activation functions and gradient flows, with convergence guaranteed by Lojasiewicz the…
A residual-iteration framework for alternating projections between affine subspaces
Nguyen T. Thao
The paper reformulates alternating projections between two affine subspaces as a least‑squares problem, introduces a residual‑state iteration framework that includes Landweber, ste…
NGMRES convergence analysis and proof of acceleration for contractive and noncontractive iterations
Y. He, L. Rebholz, M. Xiao
The paper provides the first theoretical convergence analysis of nonlinear GMRES (NGMRES) for both contractive and noncontractive fixed‑point iterations, identifying the ratio‑gain…
Multiscale Methods for Discretized Continuous Optimization: Convergence and Cost Analysis
Nicholas J. E. Richardson, Noah Marusenko, Michael P. Friedlander
The paper studies a multiscale algorithm that solves a sequence of increasingly fine discretizations of continuous optimization problems, using coarse solutions to warm‑start finer…
Quantitative asymptotic regularity and -asymptotic regularity for the inexact generalized Halpern iteration
Nicoleta Dumitru, Laurentiu Leustean
The paper uses proof‑mining techniques to derive explicit quantitative bounds on the asymptotic and T‑asymptotic regularity of an inexact generalized Halpern iteration, a viscosity…
Global Convergence of the Return Dynamics in the Class
Mohammed Barkatou, Mohamed El Morsalani
The paper studies a return map defined on domains with a fixed convex core, showing that its dynamics act like an adaptive gradient descent on the domain’s thickness function and c…
Adaptive Metrics for Norm-Minimization-Based Outer Approximation in Convex Vector Optimization
Mohammed Alshahrani
The paper proposes an adaptive-metric framework for norm‑minimization outer‑approximation algorithms in bounded convex vector optimization, proving convergence rates for any inner‑…
Semismooth Newton methods for degenerate polyhedral projection
Chao Ding, Fuxiaoyue Feng, Xudong Li
The paper develops dual semismooth Newton algorithms for degenerate polyhedral projection problems by exploiting a primal‑dual lifted representation that ensures nonsingular genera…
Hermite spectral approximation for functions with endpoint singularities using exponential transforms
Haiyong Wang
The paper proposes Hermite spectral approximations for functions with endpoint singularities using single, double, and error‑function exponential transforms, provides convergence a…
Nonasymptotic Analysis of Accelerated Methods With Inexact Oracle Under Absolute Error Bound
Yin Liu, Sam Davanloo Tajbakhsh
The paper derives explicit nonasymptotic convergence bounds for two accelerated first‑order methods applied to smooth convex problems when gradients are accessed with bounded absol…
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