On the nonmonotone line search in gradient sampling methods for nonconvex and nonsmooth optimization

• Grant number: 13/14615-7
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: October 01, 2013
• End date: February 28, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Sandra Augusta Santos
• Grantee: Lucas Eduardo Azevedo Simões
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 13/05475-7 - Computational methods in optimization, AP.TEM

Abstract

Recently, optimization problems involving nonsmooth and locally Lipschitz functions have been subject of increasing interest and investigation. Algorithms developed for solving these problems rely on the construction of a sequence of search directions from a sampling of differentials around the current iterate.In this project we propose to study a subject that is complementary to the upgrading of the search directions. As the construction of sophisticated directions has matured enough, both theoretically and practically, we believe that the development of techniques designed to relieve the computational cost of the line search would be a natural area to be explored. In particular, the primary target of our efforts will be the theoretical-practical development of techniques of nonmonotone line search for problems in nonsmooth optimization.

Scientific publications

(4)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

HELOU, ELIAS S.; SIMOES, LUCAS E. A.. epsilon-subgradient algorithms for bilevel convex optimization. INVERSE PROBLEMS, v. 33, n. 5, MAY 2017. (13/07375-0, 11/02219-4, 13/14615-7, 13/16508-3)

HELOU, ELIAS S.; SANTOS, SANDRA A.; SIMOES, LUCAS E. A.. A fast gradient and function sampling method for finite-max functions. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, v. 71, n. 3, p. 673-717, DEC 2018. (13/05475-7, 13/07375-0, 16/22989-2, 13/16508-3, 13/14615-7)

HELOU, ELIAS SALOMAO; SANTOS, SANDRA A.; SIMOES, LUCAS E. A.. On the Local Convergence Analysis of the Gradient Sampling Method for Finite Max-Functions. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, v. 175, n. 1, p. 137-157, OCT 2017. (13/07375-0, 13/05475-7, 16/22989-2, 13/14615-7)

HELOU, ELIAS SALOMAO; SANTOS, SANDRA A.; SIMOES, LUCAS E. A.. On the differentiability check in gradient sampling methods. OPTIMIZATION METHODS & SOFTWARE, v. 31, n. 5, p. 983-1007, OCT 2016. (13/16508-3, 13/05475-7, 13/14615-7, 13/07375-0)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

SIMÕES, Lucas Eduardo Azevedo. Técnicas amostrais para otimização não suave. 2017. Doctoral Thesis - Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica Campinas, SP.