Author:
Hu Shasha,Xu Yihong,Zhang Yuhan
Abstract
<p style='text-indent:20px;'>The concepts of weakly efficient solutions and globally efficient solutions are introduced for constrained set-valued equilibrium problems with variable ordering structures. By applying the second-order tangent epiderivative and a nonlinear functional, necessary optimality conditions for weakly efficient solutions and globally efficient solutions are established without any convexity assumption. Under the cone-convexity of the objective and constraint functions, sufficient optimality conditions are given. In addition, the tangent derivatives of objective and constraint functions are separated. Simultaneously, a unified necessary and sufficient optimality conditions for weakly efficient solutions is derived, and the same goes for globally efficient solutions. In particular, we give specific examples to illustrate the optimality conditions, respectively.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Control and Optimization,Strategy and Management,Business and International Management,Applied Mathematics,Control and Optimization,Strategy and Management,Business and International Management
Reference14 articles.
1. J.-P. Aubin and H. Frankowska, Set-Valued Analysis, Systems & Control: Foundations & Applications, 2. Birkhäuser Boston, Inc., Boston, MA, 1990.
2. G. Y. Chen.Existence of solutions for a vector variational inequality: An extension of the Hartmann-Stampacchia theorem, J. Optim. Theory Appl., 74 (1992), 445-456.
3. G. Y. Chen, X. Q. Yang.Characterizations of variable domination structures via nonlinear scalarization, J. Optim. Theory Appl., 112 (2002), 97-110.
4. M. Durea, R. Strugariu, C. Tammer.On set-valued optimization problems with variable ordering structure, J. Glob. Optim., 61 (2015), 745-767.
5. G. Eichfelder, Variable ordering structures in vector optimization, Recent Developments in Vector Optimization, Vector Optim., Springer, Berlin, (2012), 95–126.
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献