| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [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
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | Trends in Computational and Applied Mathematics; v. 25, 2024-11-11. |
| Abstract | |
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) | |
| 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 |