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

Grant number: 13/14615-7
Support type:Scholarships in Brazil - Doctorate
Effective date (Start): October 01, 2013
Effective date (End): February 28, 2017
Field of knowledge:Physical Sciences and Mathematics - Mathematics
Principal Investigator:Sandra Augusta Santos
Grantee:Lucas Eduardo Azevedo Simões
Home 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


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.; 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. Web of Science Citations: 0.
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. Web of Science Citations: 1.
HELOU, ELIAS S.; SIMOES, LUCAS E. A. epsilon-subgradient algorithms for bilevel convex optimization. INVERSE PROBLEMS, v. 33, n. 5 MAY 2017. Web of Science Citations: 1.
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. Web of Science Citations: 4.
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, Instituto de Matemática Estatística e Computação Científica.

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