关于非平滑优化中确定性梯度采样收敛性的说明

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Computational Optimization and Applications Pub Date : 2024-02-06 DOI:10.1007/s10589-024-00552-0

Bennet Gebken

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引用次数: 0

摘要

在计算非光滑优化问题的下降方向时，近似子微分是主要任务之一。在本文中，我们提出了一种针对弱下半滑函数的二分法，该方法能够计算新的子梯度，从而在计算的下降方向不充分的情况下改进给定的近似值。结合最近提出的确定性梯度采样方法，这将产生一种确定性的、可证明收敛的近似子微分方法，用于计算下降方向。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

A note on the convergence of deterministic gradient sampling in nonsmooth optimization

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A note on the convergence of deterministic gradient sampling in nonsmooth optimization

Approximation of subdifferentials is one of the main tasks when computing descent directions for nonsmooth optimization problems. In this article, we propose a bisection method for weakly lower semismooth functions which is able to compute new subgradients that improve a given approximation in case a direction with insufficient descent was computed. Combined with a recently proposed deterministic gradient sampling approach, this yields a deterministic and provably convergent way to approximate subdifferentials for computing descent directions.

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来源期刊

Computational Optimization and Applications 数学-应用数学

CiteScore

3.70

自引率

9.10%

发文量

审稿时长

10 months

期刊介绍： Computational Optimization and Applications is a peer reviewed journal that is committed to timely publication of research and tutorial papers on the analysis and development of computational algorithms and modeling technology for optimization. Algorithms either for general classes of optimization problems or for more specific applied problems are of interest. Stochastic algorithms as well as deterministic algorithms will be considered. Papers that can provide both theoretical analysis, along with carefully designed computational experiments, are particularly welcome. Topics of interest include, but are not limited to the following: Large Scale Optimization, Unconstrained Optimization, Linear Programming, Quadratic Programming Complementarity Problems, and Variational Inequalities, Constrained Optimization, Nondifferentiable Optimization, Integer Programming, Combinatorial Optimization, Stochastic Optimization, Multiobjective Optimization, Network Optimization, Complexity Theory, Approximations and Error Analysis, Parametric Programming and Sensitivity Analysis, Parallel Computing, Distributed Computing, and Vector Processing, Software, Benchmarks, Numerical Experimentation and Comparisons, Modelling Languages and Systems for Optimization, Automatic Differentiation, Applications in Engineering, Finance, Optimal Control, Optimal Design, Operations Research, Transportation, Economics, Communications, Manufacturing, and Management Science.