向量优化问题ε-弱有效解的Lagrange乘子定理  

A Lagrangian Multiplier Theorem of ε-weakly Efficient Solutions in Vector Optimization Problems with Set-valued Maps

作　　者：廖伟[1] 赵克全[1] 

机构地区：[1]重庆师范大学数学学院,重庆401331

出　　处：《重庆师范大学学报（自然科学版）》2013年第6期22-24,共3页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.11301574;No.11271391;No.11171363);重庆市自然科学基金(No.CSTC2012JJA00002)

摘　　要：本文在邻近锥次似凸性假设下,建立了集值映射向量优化问题ε-弱有效解的Lagrange乘子定理。首先,利用择一性定理,给出了集值优化问题ε-弱有效解的一个必要性条件。进一步,建立了集值优化问题ε-弱有效解的充分必要条件。最后,在邻近次似凸性假设下,建立了集值映射向量优化问题ε-弱有效解的Lagrange乘子定理。本文的主要结果推广了已有文献中的相应结果到近似解的情形,同时将次似凸性条件减弱到邻近次似凸的假设下。In this paper, we establish a Lagrangian multiplier theorem of ε-weakly efficient solutions in vector optimization problems with set-valued maps under the assumption of nearly cone-subconvexlike. Firstly, a necessary condition of e-weakly efficient solu-tions is given in vector optimization problems with set-valued maps using an alternative theorem. Moreover, a sufficient and necessa-ry condition of s-weakly efficient solutions is given. Finally, under the assumption of nearly cone-subconvexlike, a Lagrangian multi-plier theorem of ε-weakly efficient solutions is established for vector optimization problems with set-valued maps. The main results in this article extend the corresponding results in [6] to the approximate and meanwhile the convexity condition of [6] is reduced to the nearly cone-subconvexlike assumptions.

关 键 词：集值向量优化 ε-弱有效解 LAGRANGE乘子定理 

分 类 号：O221.6[理学—运筹学与控制论]