对带误差项的广义集值变分包含的近似点算法  

Perturbed Proximal Point Algorithm for Generalized Set-Valued Variational Inclusion with Errors

作　　者：尚明生[1] 王庆先[1] 吴鲜[2] 

机构地区：[1]四川师范学院数学系,四川南充637002 [2]云南师范大学数学系,云南昆明650092

出　　处：《数学学报（中文版）》2001年第4期753-760,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目;四川省教委基金资助项目

摘　　要：研究一类新的广义集值变分包含：０∈Ｎ（ｗ，ｙ）＋Ａ（ｚ，ｕ），它包合了近几年许多作者所作的变分包合问题．在实Ｈｉｌｂｅｒｔ空间中，利用极大单调算子的性质，建立了广义集值变分包合和不动点问题间的等价性．利用这种等价性，建立了一些摄动迭代算法，并证明了近似解序列强收敛于精确解．本文的算法和结果改进和一般化了最近许多文章中相应的算法和结果．This paper studied a new generalized set-valued variational inclusions: 0 ∈ N(w,y) + A(z,u), which included many variational inclusions studied by others in recent years. Using the resolvent technique, we established the equivalence between the generalized set-valued variational inclusions and the fixed point problems, and some perturbed iterative algorithms, proved that its proximate solution converge to its exact solution in real Hilbert space. Our results improve and generalized many known corresponding algorithms and results.

关 键 词：广义集值变分包含 集值算子 摄动迭代算法 收敛性 极大单调算子 不动点问题 强收敛 精确解 实HILBERT空间 

分 类 号：O177.91[理学—数学]