International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 15, Article ID 26808, 16 pages
doi:10.1155/IJMMS/2006/26808

Some relations between variational-like inequalities and efficient solutions of certain nonsmooth optimization problems

Lucelina Batista Santos1 , Marko A. Rojas-Medar2 and Antonio Rufián-Lizana3

1Departamento de Matemática, Universidade Federal do Paraná, CP 19081 CEP, Curitiba 81531-990, Paraná, Brazil
 2Departamento de Matemática Aplicada, Universidade Estadual de Campinas, CP 6065, Campinas 13083-859, São Paulo, Brazil
 3Departamento de Estadística e Investigación Operativa, Universidad de Sevilla, Sevilla 41012, Spain

Abstract

We study the equivalence between the solutions of the variational-like inequality problem and the solutions of certain nonsmooth and nonconvex vectorial optimization problem.