Copyright © 2011 Y. D. Xu and S. J. Li. 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

A scalarization theorem and two Lagrange multiplier theorems are established for tightly proper efficiency in vector optimization involving nearly cone-subconvexlike set-valued maps. A dual is proposed, and some duality results are obtained in terms of tightly properly efficient solutions. A new type of saddle point, which is called tightly proper saddle point of an appropriate set-valued Lagrange map, is introduced and is used to characterize tightly proper efficiency.