On the Local Convergence Analysis of the Gradient Sampling Method for Finite Max-Functions

Author(s)

Helou, Elias Salomao ^[1] ; Santos, Sandra A. ^[2] ; Simoes, Lucas E. A. ^[2]

Affiliation

^[1] Univ Sao Paulo, Inst Math Sci & Computat, Sao Carlos, SP - Brazil

^[2] Univ Estadual Campinas, Dept Appl Math, Campinas, SP - Brazil

• Document type: Journal article
• Source: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS; v. 175, n. 1, p. 137-157, OCT 2017.
• Web of Science Citations: 1

Abstract

The gradient sampling method is a recently developed tool for solving unconstrained nonsmooth optimization problems. Using just first-order information about the objective function, it generalizes the steepest descent method, one of the most classical methods for minimizing a smooth function. This study aims at determining under which circumstances one can expect the same local convergence result of the Cauchy method for the gradient sampling algorithm under the assumption that the problem is stated by a finite max-function around the optimal point. Additionally, at the end, we show how to practically accomplish the required hypotheses during the execution of the algorithm. (AU)

• FAPESP's process: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry
• Grantee: Francisco Louzada Neto
• Support Opportunities: Research Grants - Research, Innovation and Dissemination Centers - RIDC
• FAPESP's process: 13/05475-7 - Computational methods in optimization
• Grantee: Sandra Augusta Santos
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 16/22989-2 - A sampling method for constrained nonsmooth optimization problems
• Grantee: Lucas Eduardo Azevedo Simões
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 13/14615-7 - On the nonmonotone line search in gradient sampling methods for nonconvex and nonsmooth optimization
• Grantee: Lucas Eduardo Azevedo Simões
• Support Opportunities: Scholarships in Brazil - Doctorate