把可微规划的Mond Weir对偶推广到非光滑规划的广义Mond Weir对偶 ,然后在广义 η 严格伪凸函数 ,广义 η 伪凸函数、广义 η 拟凸函数和广义 η 弱拟凸函数四类广义凸函数条件下 ,讨论了该非光滑规划的广义Mond Weir对偶 ,得到了相应...把可微规划的Mond Weir对偶推广到非光滑规划的广义Mond Weir对偶 ,然后在广义 η 严格伪凸函数 ,广义 η 伪凸函数、广义 η 拟凸函数和广义 η 弱拟凸函数四类广义凸函数条件下 ,讨论了该非光滑规划的广义Mond Weir对偶 ,得到了相应的弱对偶定理。展开更多
Hanson and Mond have grven sets of necessary and sufficient conditions for optimality in constrained optimization by introducing classes of generalized functions, called type Ⅰ functions. Recently, Bector definded un...Hanson and Mond have grven sets of necessary and sufficient conditions for optimality in constrained optimization by introducing classes of generalized functions, called type Ⅰ functions. Recently, Bector definded univex functions, a new class of functions that unifies several concepts of generalized convexity. In this paper, additional conditions are attached to the Kuhn Tucker conditions giving a set of conditions which are both necessary and sufficient for optimality in constrained optimization, under appropriate constraint qualifications.展开更多
A class of functions and a sort of nonlinear programming called respectively E-convex functions and E-convex programming were presented and studied recently by Youness in [1], In this paper, we point out the most resu...A class of functions and a sort of nonlinear programming called respectively E-convex functions and E-convex programming were presented and studied recently by Youness in [1], In this paper, we point out the most results for .E-convex functions and E-convex programming in [1] are not true by six counter examples.展开更多
We focus on second order duality for a class of multiobjective programming problem subject to cone constraints. Four types of second order duality models are formulated. Weak and strong duality theorems are establishe...We focus on second order duality for a class of multiobjective programming problem subject to cone constraints. Four types of second order duality models are formulated. Weak and strong duality theorems are established in terms of the generalized convexity, respectively. Converse duality theorems, essential parts of duality theory, are presented under appropriate assumptions. Moreover, some deficiencies in the work of Ahmad and Agarwal(2010) are discussed.展开更多
文摘Hanson and Mond have grven sets of necessary and sufficient conditions for optimality in constrained optimization by introducing classes of generalized functions, called type Ⅰ functions. Recently, Bector definded univex functions, a new class of functions that unifies several concepts of generalized convexity. In this paper, additional conditions are attached to the Kuhn Tucker conditions giving a set of conditions which are both necessary and sufficient for optimality in constrained optimization, under appropriate constraint qualifications.
基金National Natural Science Foundation of China(10261001)Science Foundation of Guangxi(0236001)
文摘A class of functions and a sort of nonlinear programming called respectively E-convex functions and E-convex programming were presented and studied recently by Youness in [1], In this paper, we point out the most results for .E-convex functions and E-convex programming in [1] are not true by six counter examples.
基金supported by National Natural Science Foundation of China (Grant Nos. 11431004, 11271391 and 11201511)the Project of Chongqing Science and Technology Committee (Grant No. cstc2014pt-sy00001)Theoretical Foundation and Application Procedure of Environmental Data Envelopment Analysis Model (Grant No. B-Q22L)
文摘We focus on second order duality for a class of multiobjective programming problem subject to cone constraints. Four types of second order duality models are formulated. Weak and strong duality theorems are established in terms of the generalized convexity, respectively. Converse duality theorems, essential parts of duality theory, are presented under appropriate assumptions. Moreover, some deficiencies in the work of Ahmad and Agarwal(2010) are discussed.
