弧连通锥-凸数学规划的最优性条件  

Optimality Conditions for Mathematical Programming Involving Arcwise Connected Cone-Convex Functions

作　　者：陈炜[1] 余国林[2] 

机构地区：[1]首都经济贸易大学信息学院,北京100070 [2]北方民族大学信息与系统科学研究所,宁夏银川750021

出　　处：《数学的实践与认识》2010年第6期128-133,共6页Mathematics in Practice and Theory

基　　金：国家青年自然科学基金(10901004);北京市教委人文社科项目(SM2009100038005);北京市属高等学校人才强教深化计划项目(RHR201007117);国家民委自然科学基金(09BF06);宁夏自然科学基金(NZ0959)

摘　　要：在弧连通锥-凸假设下讨论Hausdorff局部凸空间中的一类数学规划的最优性条件问题.首先,利用择一定理得到了锥约束标量优化问题的一个必要最优性条件.其次,利用凸集分离定理证明了无约束向量优化问题关于弱极小元的标量化定理和一个一致的充分必要条件.所得结果深化和丰富了最优化理论及其应用的内容.This note deals with a kind of mathematical programming problems where all functions involved are arcwise connected cone-convex in HausdorfF locally convex spaces.First,by using the alternative theorem,a theorem of optimality necessary condition for a scalar optimization problem with cone-constrained is established.Then,The scalarization theorem and the unified necessary and sufficient optimality conditions are proposed for weakly minimum in a vector optimization problem through the separation theorem.The results deepen and enrich the content of optimization theory and application.

关 键 词：数学规划 最优性条件 弧连通锥-凸函数 弱极小元 标量化 

分 类 号：O224[理学—运筹学与控制论]