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A sequential optimality condition for Mathematical Programs with equilibrium constraints based on a nonsmooth formulation

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Author(s):
Helou, Elias S. ; Santos, Sandra A. ; Simoes, Lucas E. A.
Total Authors: 3
Document type: Journal article
Source: IMA JOURNAL OF NUMERICAL ANALYSIS; v. N/A, p. 30-pg., 2022-05-18.
Abstract

Explicitly nonsmooth reformulations of mathematical programs with equilibrium constraints (MPEC) described by smooth functions are investigated. A sequential optimality condition (epsilon-ANOC) previously developed for nonsmooth optimization problems is adapted to suit the reformulations under analysis. Relationships between epsilon-ANOC and sequential optimality conditions especially crafted for MPEC are established. It is revealed that approaches developed for nonsmooth optimization improve the understanding of smooth problems with ill-conditioned geometries, which is the case for MPEC. Moreover, based on the availability of algorithms capable of generating epsilon-ANOC sequences, illustrative experiments are reported in which difficult problems are successfully solved. (AU)

FAPESP's process: 18/24293-0 - Computational methods in optimization
Grantee:Sandra Augusta Santos
Support Opportunities: Research Projects - Thematic Grants
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: 16/22989-2 - A sampling method for constrained nonsmooth optimization problems
Grantee:Lucas Eduardo Azevedo Simões
Support Opportunities: Scholarships in Brazil - Post-Doctoral