Abstract and Applied Analysis
Volume 2007 (2007), Article ID 61296, 11 pages
doi:10.1155/2007/61296
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
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.