一类非光滑锥约束规划问题的混合对偶  

Mixed Dual for a Class of Non-smooth Programming Problems

作　　者：唐莉萍[1] 赵克全[1] 

机构地区：[1]重庆师范大学数学学院,重庆400047

出　　处：《重庆师范大学学报（自然科学版）》2010年第5期5-8,共4页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.10771228);重庆师范大学青年基金项目(No.08XLQ01)

摘　　要：研究了非光滑锥约束规划问题的混合对偶模型的弱对偶、强对偶和逆对偶结果。在K-广义不变凸性、K-广义伪不变凸性条件下证明了两个弱对偶定理;在K-广义不变凸性条件下,利用广义Slater约束规格给出了强对偶定理;在K-非光滑不变凸性和非光滑伪不变凸性下研究了该类模型的逆对偶定理。In recent years,nonsmooth analysis becomes one of the research topics.Dual problem plays an important role in programming problem,especially in nonsmooth programming problem over cones.In this paper,we focus on the mixed dual model for nonsmooth multi-objective programming with respect to cones constraints.Three dual theorems for this programming problem are given,which are weak dual theorem,strong dual theorem and converse dual theorem.Firstly,two weak dual theorems under K-generalization invexity and K-generalization pseudoinvexity are proved;then,one strong dual theorem is given under generalized Slater constraint qualification and nonsmooth cone-invexity;finally,converse theorem is proved under K-nonsmooth invexity and pseudoinvexity.

关 键 词：K-广义不变凸性 混合对偶 非光滑锥约束规划问题 

分 类 号：O221.2[理学—运筹学与控制论] O174.2[理学—数学]