Journal of Inequalities and Applications
Volume 2011 (2011), Article ID 839679, 24 pages
Research Article

Tightly Proper Efficiency in Vector Optimization with Nearly Cone-Subconvexlike Set-Valued Maps

College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China

Received 26 September 2010; Revised 17 December 2010; Accepted 7 January 2011

Academic Editor: Kok Teo

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.


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.