Mathematical Problems in Engineering
Volume 2016, Article ID 8462602, 14 pages
http://dx.doi.org/10.1155/2016/8462602
Sufficiency and Duality for Multiobjective Programming under New Invexity
College of Science, Xi’an University of Science and Technology, Xi’an 710054, China
Received 24 March 2016; Accepted 28 August 2016
Academic Editor: Yakov Strelniker
Copyright © 2016 Yingchun Zheng and Xiaoyan Gao. 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 class of multiobjective programming problems including inequality constraints is considered. To this aim, some new concepts of generalized -type I and -type II functions are introduced in the differentiable assumption by using the sublinear function . These new functions are used to establish and prove the sufficient optimality conditions for weak efficiency or efficiency of the multiobjective programming problems. Moreover, two kinds of dual models are formulated. The weak dual, strong dual, and strict converse dual results are obtained under the aforesaid functions.