International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 26808, 16 pages

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

Lucelina Batista Santos,1 Marko A. Rojas-Medar,2 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

Received 28 November 2005; Revised 4 June 2006; Accepted 21 June 2006

Copyright © 2006 Lucelina Batista Santos et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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