{"title":"A note on the convergence of deterministic gradient sampling in nonsmooth optimization","authors":"Bennet Gebken","doi":"10.1007/s10589-024-00552-0","DOIUrl":null,"url":null,"abstract":"<p>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.</p>","PeriodicalId":55227,"journal":{"name":"Computational Optimization and Applications","volume":"158 1","pages":""},"PeriodicalIF":1.6000,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Optimization and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10589-024-00552-0","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
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.
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.
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