非光滑B-预不变凸优化问题的解集刻画(英文)  

On Characterizing Solution Sets of Nonsmooth B-Preinvex Optimization Problems

作　　者：万轩[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）》2012年第6期1-5,共5页Journal of Chongqing Normal University:Natural Science

基　　金：The National Science Foundation of China(No.11171363);the Special Fund of Chongqing Key Laboratory(No.CSTC2011KLORSE02);the Education Committee Research Foundation of Chongqing(No.KJ110625)

摘　　要：给出了具有不等式约束的非光滑B-预不变凸优化问题的最优解集的各种刻画。首先,利用Clarke次微分建立了该优化问题最优解的充分必要条件;再讨论了该优化问题在其解集S上的一个性质:最后建立了该优化问题解集的5种等价形式,即S={x∈M〈^ξ,η(z,x)〉=0,^ξ∈cf(x)=(x∈M〈^ξ,η(z,x)〉≥0,^ξ∈cf(x)}={x∈M〈^ξ,η(x,z)〉=〈^ζ,η(z,x)〉,^ξ∈C(z),^ζ∈cf(x)}={x∈M〈^ξ,η(x,z)〉≥〈^ζ,η(z,x)〉,^ξ∈C(z),^ζ∈cf(x)}={x∈M〈^ξ,η(x,z)〉=〈^ζ,η(z,x)〉=0,^ξ∈C(z),^ζ∈cf(x)},并举例验证这5个集合都相等,为S={0}。In this paper, various characterizations lems with inequality constrains are given. Firstly condition for this kind of optimization problem; strained B-preinvex optimization proble; finally, is, i.e. S = {0} . of optimal solution sets of nonsmooth B-preinvex optimization prob- , making use of Clarke＇s subdifferential, we establish the optimality secondly, we presented a property about the solution set S of con five equivalent characterizations of the solution set are obtained, that = （x An example is given E MI to illustrate that five solution sets are

关 键 词：非光滑B-预不变凸优化 Clarke次微分 解集 

分 类 号：O221.2[理学—运筹学与控制论]