Banach空间中一类广义扰动优化问题最优解的存在性  

Existence of optimal solution to a class of generalized perturbed optimization problems in Banach spaces

作　　者：何金苏[1] 

机构地区：[1]浙江师范大学数理与信息工程学院,浙江金华321004

出　　处：《浙江师范大学学报（自然科学版）》2010年第2期138-141,共4页Journal of Zhejiang Normal University:Natural Sciences

基　　金：国家自然科学基金资助项目(10671175)

摘　　要：设X是Banach空间,G是X的非空闭子集,C是X的有界闭凸子集,且0是C的内点,J:G→R是下半连续下有界函数;取x∈X,设φ(x)=infz∈G(J(z)+pC(x-z)).研究了广义扰动优化问题infz∈G(J(z)+pC(x-z))(记作(JC,x)-inf)解的存在性;讨论了函数φ(x)的单侧导数与(JC,x)-inf问题解的存在性的关系;给出了当C紧局一致凸,φ(x)的单侧导数等于1或-1时,(JC,x)-inf问题有解.所得结果推广了已有的一些结果.Let X be a Banach space and G be a nonempty closed subset of X and C be a closed bounded convex subset of X with 0 being an interior point of C.Suppose J：G→Rbe a lower semicontinuous function bounded from below;For a point x∈X,let φ（x）=infz∈G（J（z）＋p-C（x-z））.The problem of the existence of the generalized optimal solution of the perturbed optimization problem infz∈G（J（z）＋p-C（x-z））（denoted by（J-C,x）-inf） was studied.The relationship between derivatives of φ（x） and the existence of the problem（J-C,x）-inf was also discussed.The existence of the problem（J-C,x）-inf when C was compactly locally uniformly convex and the one-side diretional derivative of φ（x） equaled to 1 or-1 was obtained,which extended some known results.

关 键 词：紧局一致凸 JC-逼近紧 JC-极小化序列 最优值函数 

分 类 号：O174.41[理学—数学]