带有模糊集值映象的一般混合拟变分包含的扰动近似点算法(英文)  

Perturbed Proximal Point Algorithm for General Quasi-Variational Inclusions with Fuzzy Set-Valued Mappings

作　　者：金茂明[1] 

机构地区：[1]涪陵师范学院数学系,重庆涪陵408003

出　　处：《运筹学学报》2005年第3期31-38,共8页Operations Research Transactions

基　　金：This research is supported by the National Natural Science Foundation of China(69903012, 60216263) National 863 Project 2003AA148040the Educational Science Foundation of Chongqing, Chongqing of China (KJ051307)

摘　　要：本文引入一类新的带有模糊集值映象的一般混合拟变分包.在Hilbert空间中,利用极大η-单调映象的预解算子技巧,建立了这类变分包与不动点的等价性.利用这种等价性,构造了一些新的扰动近似点算法,并证明了由此算法所产生的迭代序列的收敛性.这些定理改进,统一和推广了近期文献中许多重要结果.The purpose of this paper is to introduce a new class of general mixed quasivariational inclusions with fuzzy set-valued mappings. We establish the equivalence between this class of variational inclusions and the fixed point problems by employing the resolvent operator technique for maximal η-monotone mapping in Hilbert spaces. Using this equivalence, we construct some new perturbed proximal point algorithms and prove the convergence of iterative sequences generated by the algorithms. These theorems improve, unify and generalize many important results in recent literature.

关 键 词：运筹学 极大Η-单调映象 模糊集值映象 收敛性 近似点算法 变分包含 扰动 混合 Hilbert空间 预解算子 单调映象 迭代序列 

分 类 号：O176[理学—数学] O177.91[理学—基础数学]