1. On the Continuous-Time Complementarity Problem
- Author
-
M. R. C. do Monte and V. A. de Oliveira
- Subjects
continuous-time complementarity problem, variational inequalities problem, continuous-time programming problems ,Mathematics ,QA1-939 - 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.
- Published
- 2024
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