Operator h-preinvex functions are introduced and a refinement of HermiteHadamard type inequalities for such functions is established. Results proved in this paper are more general and some known results are special ca...Operator h-preinvex functions are introduced and a refinement of HermiteHadamard type inequalities for such functions is established. Results proved in this paper are more general and some known results are special cases.展开更多
The optimality Kuhn-Tucker condition and the wolfe duality for the preinvex set-valued optimization are investigated. Firstly, the concepts of alpha-order G-invex set and the alpha-order S-preinvex set-valued function...The optimality Kuhn-Tucker condition and the wolfe duality for the preinvex set-valued optimization are investigated. Firstly, the concepts of alpha-order G-invex set and the alpha-order S-preinvex set-valued function were introduced, from which the properties of the corresponding contingent cone and the alpha-order contingent derivative were studied. Finally, the optimality Kuhn-Tucker condition and the Wolfe duality theorem for the alpha-order S-preinvex set-valued optimization were presented with the help of the alpha-order contingent derivative.展开更多
基金The NSF(11801342) of Chinathe Foundation(18JK0116) of Shaanxi Educational Committee
文摘Operator h-preinvex functions are introduced and a refinement of HermiteHadamard type inequalities for such functions is established. Results proved in this paper are more general and some known results are special cases.
基金Supported by Key Disciplines of Shanghai Municipality（Operations Research and Cybernetics）（S30104） Supported by Shanghai Leading Academic Discipline Project（J50101） Supported by National Science Foundation Project of CQCSTC（2009BB3372）
基金Project supported by the National Natural Science Foundation of China (No. 10371024) the Natural Science Foundation of Zhejiang Province (No.Y604003)
文摘The optimality Kuhn-Tucker condition and the wolfe duality for the preinvex set-valued optimization are investigated. Firstly, the concepts of alpha-order G-invex set and the alpha-order S-preinvex set-valued function were introduced, from which the properties of the corresponding contingent cone and the alpha-order contingent derivative were studied. Finally, the optimality Kuhn-Tucker condition and the Wolfe duality theorem for the alpha-order S-preinvex set-valued optimization were presented with the help of the alpha-order contingent derivative.
基金This research was partially supported by the National Natural Science Foundation of China(Grant No.10171118,10471159)the key project of the Chinese Ministry of Education,Supported by Program for New Century Excellent Talents in University.
基金This research was partially supported by the National Natural Science Foundation of China (Grant No.10171118)Education Committee project Research Foundation of Chongqing (Grant No. 030801)National Natural Science Foundation of Chongqing (Grant No. 8904)
