Scholarship 16/22989-2 - Otimização restrita, Problemas de otimização - BV FAPESP
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A sampling method for constrained nonsmooth optimization problems

Grant number: 16/22989-2
Support Opportunities:Scholarships in Brazil - Post-Doctoral
Start date until: April 01, 2017
End date until: March 31, 2021
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Applied Mathematics
Agreement: Coordination of Improvement of Higher Education Personnel (CAPES)
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: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

Abstract

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)

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Scientific publications (8)
(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.. Analysis of a New Sequential Optimality Condition Applied to Mathematical Programs with Equilibrium Constraints. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, v. 185, n. 2, . (13/07375-0, 18/24293-0, 16/22989-2)
HELOU, ELIAS S.; SANTOS, SANDRA A.; SIMOES, LUCAS E. A.. A sequential optimality condition for Mathematical Programs with equilibrium constraints based on a nonsmooth formulation. IMA JOURNAL OF NUMERICAL ANALYSIS, v. N/A, p. 30-pg., . (18/24293-0, 13/07375-0, 16/22989-2)
PRADO, RENAN W.; SANTOS, SANDRA A.; SIMOES, LUCAS E. A.. On the Fulfillment of the Complementary Approximate Karush-Kuhn-Tucker Conditions and Algorithmic Applications. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, v. 197, n. 2, p. 32-pg., . (18/24293-0, 13/07375-0, 16/22989-2, 19/18859-4)
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, . (13/05475-7, 13/07375-0, 16/22989-2, 13/16508-3, 13/14615-7)
HELOU, ELIAS S.; SANTOS, SANDRA A.; SIMOES, LUCAS E. A.. A NEW SEQUENTIAL OPTIMALITY CONDITION FOR CONSTRAINED NONSMOOTH OPTIMIZATION. SIAM JOURNAL ON OPTIMIZATION, v. 30, n. 2, p. 1610-1637, . (17/07265-0, 13/07375-0, 18/24293-0, 16/22989-2)
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, . (13/07375-0, 13/05475-7, 16/22989-2, 13/14615-7)
PRADO, RENAN W.; SANTOS, SANDRA A.; SIMOES, LUCAS E. A.. On the convergence analysis of a penalty algorithm for nonsmooth optimization and its performance for solving hard-sphere problems. NUMERICAL ALGORITHMS, v. N/A, p. 25-pg., . (18/24293-0, 13/07375-0, 19/18859-4, 16/22989-2)
HELOU, ELIAS S.; SANTOS, SANDRA A.; SIMOES, LUCAS E. A.. A primal nonsmooth reformulation for bilevel optimization problems. MATHEMATICAL PROGRAMMING, v. N/A, p. 29-pg., . (13/07375-0, 16/22989-2, 18/24293-0)

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