Iterative Schemes for Convex Minimization Problems with Constraints
We first introduce and analyze one implicit iterative algorithm for finding a solution of the minimization problem for a convex and continuously Fréchet differentiable functional, with constraints of several problems: the generalized mixed equilibrium problem, the system of generalized equilibrium p...
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doaj-3f3c9c515e444387bffa58f3560df2d42020-11-24T22:37:15ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/209372209372Iterative Schemes for Convex Minimization Problems with ConstraintsLu-Chuan Ceng0Cheng-Wen Liao1Chin-Tzong Pang2Ching-Feng Wen3Department of Mathematics, Shanghai Normal University, and Scientific Computing Key Laboratory of Shanghai Universities, Shanghai 200234, ChinaDepartment of Food and Beverage Management, Vanung University, Chung-Li 320061, TaiwanDepartment of Information Management and Innovation Center for Big Data and Digital Convergence, Yuan Ze University, Chung-Li 32003, TaiwanCenter for Fundamental Science, Kaohsiung Medical University, Kaohsiung 807, TaiwanWe first introduce and analyze one implicit iterative algorithm for finding a solution of the minimization problem for a convex and continuously Fréchet differentiable functional, with constraints of several problems: the generalized mixed equilibrium problem, the system of generalized equilibrium problems, and finitely many variational inclusions in a real Hilbert space. We prove strong convergence theorem for the iterative algorithm under suitable conditions. On the other hand, we also propose another implicit iterative algorithm for finding a fixed point of infinitely many nonexpansive mappings with the same constraints, and derive its strong convergence under mild assumptions.http://dx.doi.org/10.1155/2014/209372 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Lu-Chuan Ceng Cheng-Wen Liao Chin-Tzong Pang Ching-Feng Wen |
spellingShingle |
Lu-Chuan Ceng Cheng-Wen Liao Chin-Tzong Pang Ching-Feng Wen Iterative Schemes for Convex Minimization Problems with Constraints Abstract and Applied Analysis |
author_facet |
Lu-Chuan Ceng Cheng-Wen Liao Chin-Tzong Pang Ching-Feng Wen |
author_sort |
Lu-Chuan Ceng |
title |
Iterative Schemes for Convex Minimization Problems with Constraints |
title_short |
Iterative Schemes for Convex Minimization Problems with Constraints |
title_full |
Iterative Schemes for Convex Minimization Problems with Constraints |
title_fullStr |
Iterative Schemes for Convex Minimization Problems with Constraints |
title_full_unstemmed |
Iterative Schemes for Convex Minimization Problems with Constraints |
title_sort |
iterative schemes for convex minimization problems with constraints |
publisher |
Hindawi Limited |
series |
Abstract and Applied Analysis |
issn |
1085-3375 1687-0409 |
publishDate |
2014-01-01 |
description |
We first introduce and analyze one implicit iterative algorithm for finding a solution of the minimization problem for a convex and continuously Fréchet differentiable functional, with constraints of several problems: the generalized mixed equilibrium problem, the system of generalized equilibrium problems, and finitely many variational inclusions in a real Hilbert space. We prove strong convergence theorem for the iterative algorithm under suitable conditions. On the other hand, we also propose another implicit iterative algorithm for finding a fixed point of infinitely many nonexpansive mappings with the same constraints, and derive its strong convergence under mild assumptions. |
url |
http://dx.doi.org/10.1155/2014/209372 |
work_keys_str_mv |
AT luchuanceng iterativeschemesforconvexminimizationproblemswithconstraints AT chengwenliao iterativeschemesforconvexminimizationproblemswithconstraints AT chintzongpang iterativeschemesforconvexminimizationproblemswithconstraints AT chingfengwen iterativeschemesforconvexminimizationproblemswithconstraints |
_version_ |
1725717978075365376 |