Abstract and Applied Analysis
Volume 2007 (2007), Article ID 61296, 11 pages
doi:10.1155/2007/61296
Research Article
Continuous-Time Multiobjective Optimization Problems via Invexity
Departamento de Matemática Aplicada, Instituto de Matemática, Estatística e Computação Científica, UNICAMP, UNICAMP, CP 6065, Campinas 13083-859, SP, Brazil
Received 29 March 2006; Accepted 1 December 2006
Academic Editor: Nikolaos S. Papageorgiou
Copyright © 2007 Valeriano A. De Oliveira and Marko A. Rojas-Medar. 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.
Abstract
We introduce some concepts of generalized invexity for the continuous-time multiobjective programming problems, namely, the concepts of Karush-Kuhn-Tucker invexity and
Karush-Kuhn-Tucker pseudoinvexity. Using the concept of Karush-Kuhn-Tucker invexity, we study the relationship of the multiobjective problems with some related scalar problems. Further, we
show that Karush-Kuhn-Tucker pseudoinvexity is a necessary and suffcient condition for a vector Karush-Kuhn-Tucker solution
to be a weakly efficient solution.