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A sampling method for constrained nonsmooth optimization problems

Grant number: 16/22989-2
Support type:Scholarships in Brazil - Post-Doctorate
Effective date (Start): April 01, 2017
Effective date (End): July 31, 2020
Field of knowledge:Physical Sciences and Mathematics - Mathematics
Cooperation agreement: Coordination of Improvement of Higher Education Personnel (CAPES)
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:18/24293-0 - Computational methods in optimization, AP.TEM
Associated scholarship(s):17/07265-0 - Sampling techniques for constrained nonsmooth optimization problems: theory development, BE.EP.PD


Recently, optimization problems involving locally Lipschitz nonsmooth functions have gained more scientific interest. Pursuing this perspective, a method known as Gradient Sampling (GS) was developed for the solution of such unconstrained problems. Further, using the same concepts, a new sampling method was elaborated for the solution of constrained nonsmooth optimization problems, using a penalty function and the ideas developed over the years for Sequential Quadratic Programming methods. In this project, we have the goal to develop a new sampling method for constrained nonsmooth optimization problems. Our proposal involves a new penalty function, whose flexibility allows us to consider bilevel optimization problems. Since many decision-making models encompass hierarchical optimization problems, we believe that this project, besides offering a theoretical contribution, possesses an effective potentiality of application. (AU)

Scientific publications
(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.

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