Abstract and Applied Analysis
Volume 2007 (2007), Article ID 61296, 11 pages
Research Article

Continuous-Time Multiobjective Optimization Problems via Invexity

Valeriano A. De Oliveira and Marko A. Rojas-Medar

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.


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.