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