On the Continuous-Time Complementarity Problem

Autor(es)

M. R. C. DO MONTE ^[1] ; V. A. DE OLIVEIRA ^[2]

Afiliação do(s) autor(es)

^[1] Universidade Federal de Uberlândia. Instituto de Ciências Exatas e Naturais do Pontal - Brasil

^[2] Universidade Estadual Paulista. Instituto de Biociências, Letras e Ciências Exatas - Brasil

• Tipo de documento: Artigo Científico
• Fonte: Trends in Computational and Applied Mathematics; v. 25, 2024-11-11.

Resumo

ABSTRACT This work deals with solving continuous-time nonlinear complementarity problems defined on two types of nonempty closed convex cones: a polyhedral cone (positive octant) and a second-order cone. Theoretical results that establish a relationship between such problems and the variational inequalities problem are presented. We show that global minimizers of an unconstrained continuous-time programming problem are solutions to the continuous-time nonlinear complementarity problem. Moreover, a relation is set up so that a stationary point of an unconstrained continuous-time programming problem, in which the objective function involves the Fischer-Burmeister function, is a solution for the continuous-time complementarity problem. To guarantee the validity of the K.K.T. conditions for some auxiliary continuous-time problems which appear during the theoretical development, we use the linear independence constraint qualification. These constraint qualification are posed in the continuous-time context and appeared in the literature recently. In order to exemplify the developed theory, some simple examples are presented throughout the text. (AU)

• Processo FAPESP: 13/07375-0 - CeMEAI - Centro de Ciências Matemáticas Aplicadas à Indústria
• Beneficiário: Francisco Louzada Neto
• Modalidade de apoio: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs