Averaged Mappings and the Gradient-Projection Algorithm

被引：224

作者：

Xu, Hong-Kun ^{[1
,2
]}

机构：

[1] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 804, Taiwan

[2] King Saud Univ, Dept Math, Coll Sci, Riyadh 11451, Saudi Arabia

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2011年 / 150卷 / 02期

关键词：

Averaged mapping; Gradient-projection algorithm; Constrained convex minimization; Maximal monotone operator; Relaxed gradient-projection algorithm; Regularization; Minimum-norm; PROXIMAL POINT ALGORITHM; VISCOSITY APPROXIMATION METHODS; SPLIT FEASIBILITY PROBLEM; NONEXPANSIVE-MAPPINGS; STRONG-CONVERGENCE; VARIATIONAL-INEQUALITIES; ITERATIVE ALGORITHMS; NONLINEAR OPERATORS; MONOTONE-OPERATORS; BANACH-SPACES;

D O I：

10.1007/s10957-011-9837-z

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

It is well known that the gradient-projection algorithm (GPA) plays an important role in solving constrained convex minimization problems. In this article, we first provide an alternative averaged mapping approach to the GPA. This approach is operator-oriented in nature. Since, in general, in infinite-dimensional Hilbert spaces, GPA has only weak convergence, we provide two modifications of GPA so that strong convergence is guaranteed. Regularization is also applied to find the minimum-norm solution of the minimization problem under investigation.

引用

页码：360 / 378

页数：19

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