Proximal point algorithm for generalized multivalued nonlinear quasi-variational-like inclusions in Banach spaces

Ahmad R; Siddiqi AH; Khan Z

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Proximal point algorithm for generalized multivalued nonlinear quasi-variational-like inclusions in Banach spaces

机译：Banach空间中广义多值非线性拟似变分包含的近点算法

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In this paper, we define a new notion of J(n)-proxiinal mapping for a nonconvex, lower semicontinuous, n-subdifferentiable proper functional in Banach spaces. The existence and Lipschitz continuity of J(n)-proximal mapping of a lower semicontinuous, n-subdifferentiable proper functional are proved. By applying this notion, we introduce and study generalized miultivalued nonlinear cluasi-variational-like inclusions in reflexive Banach spaces and propose a proximal point algorithm for finding the approximate Solutions Of this Class of variational inclusions. The convergence criteria of the iterative sequences generated by our algorithm is discussed. Several special cases are also given. (C) 2004 Elsevier Inc. All rights reserved.

机译：在本文中，我们为Banach空间中的一个非凸的，下半连续的，n次可微分的固有函数定义了J（n）-近邻映射的新概念。证明了下半连续，n次可微分固有函数的J（n）-近映射的存在和Lipschitz连续性。通过应用这一概念，我们介绍并研究了自反Banach空间中的广义多值非线性类似变分包含，并提出了一种用于寻找此类变分包含的近似解的近点算法。讨论了我们算法生成的迭代序列的收敛准则。还给出了几种特殊情况。（C）2004 Elsevier Inc.保留所有权利。

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《Applied mathematics and computation》 |2005年第1期|共14页
作者
Ahmad R; Siddiqi AH; Khan Z;
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正文语种 eng
中图分类应用数学;
关键词
variational-like inclusions; eta-subdifferentiable; J(eta)-proximal mapping; reflexive Banach spaces; algorithm; PERTURBED ALGORITHM; INEQUALITIES; MAPPINGS;

机译：类变分包含;eta-可微;J（eta）-近映射;自反Banach空间;算法;扰动算法;不等式;MAPPINGS;

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1. Proximal point algorithm for generalized multivalued nonlinear quasi-variational-like inclusions in Banach spaces [J] . Ahmad R, Siddiqi AH, Khan Z Applied mathematics and computation . 2005,第1期

机译：Banach空间中广义多值非线性拟似变分包含的近点算法
2. A new system of generalized set-valued nonlinear mixed quasi-variational-like inclusions with (H,eta)-accretive mappings in Banach spaces [J] . Jae Ug Jeong International mathematical forum . 2010,第9a12期

机译：Banach空间中具有（H， eta）增生映射的广义集值非线性混合类拟变分包含的新系统
3. A new system of generalized nonlinear quasi-variational-like inclusions with A-monotone operators in Banach spaces [J] . Feng HR, Ding XP Journal of Computational and Applied Mathematics . 2009,第2期

机译：Banach空间中带A-单调算子的广义非线性拟似变分包含的新系统
4. New System of Quasi-variational-Like Inclusions Involving Monotone Operators in General Banach Spaces [C] . International Forum on Information Technology and Applications . 2009

机译：涉及一般Banach空间中的单调运营商的准分层夹杂物的新系统
5. Convergence of greedy -type algorithms in Banach spaces [D] . Ganichev, Mikhail 2006

机译：Banach空间中贪心类型算法的收敛性
6. Existence Results for Differential Inclusions with Nonlinear Growth Conditions in Banach Spaces [O] . Messaoud Bounkhel 2013

机译：Banach空间中具有非线性增长条件的微分包含的存在性结果
7. A new system of generalized nonlinear quasi-variational-like inclusions with A-monotone operators in Banach spaces [O] . Feng Hai Rong, Ding Xie Ping 2009

机译：Banach空间中带A-单调算子的广义非线性拟似变分包含的新系统

Proximal point algorithm for generalized multivalued nonlinear quasi-variational-like inclusions in Banach spaces

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