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Mathematical Problems in Engineering
Volume 2017, Article ID 5978130, 7 pages
https://doi.org/10.1155/2017/5978130
Research Article

ε-Properly Efficiency of Multiobjective Semidefinite Programming with Set-Valued Functions

1College of Mathematics Science, Inner Mongolia Normal University, Huhhot 010022, China
2College of Mathematics Science, Inner Mongolia University, Huhhot 010021, China

Correspondence should be addressed to Chun Hong Yuan; moc.621@9791gnohnuhcnauy

Received 10 September 2016; Revised 5 March 2017; Accepted 14 March 2017; Published 22 March 2017

Academic Editor: Thomas Hanne

Copyright © 2017 Chun Hong Yuan and Wei Dong Rong. 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

In this paper, we study the -properly efficiency of multiobjective semidefinite programming with set-valued functions. Firstly, we obtain the scalarization theorems under the condition of the generalized cone-subconvexlikeness. Then, we establish the alternative theorem which contains matrixes and vectors, the -Lagrange multiplier theorems, and the -proper saddle point theorems of the primal programming under some suitable conditions.