A Tseng’s Type Penalty Scheme for Solving Inclusion Problems Involving Linearly Composed and Parallel-Sum Type Monotone Operators

被引：8
作者：
Boţ R.I. [1 ]
Csetnek E.R. [1 ]
机构：
[1] University of Vienna, Oskar-Morgenstern-Platz 1, Vienna
来源：
Vietnam Journal of Mathematics | 2014年 / 42卷 / 4期
关键词：
Convex minimization problem; Fenchel conjugate; Fitzpatrick function; Forward–backward–forward algorithm; Infimal-convolution; Lipschitz continuous operator; Maximally monotone operator; Parallel-sum; Resolvent; Subdifferential;
D O I：
10.1007/s10013-013-0050-2
中图分类号：
学科分类号：
摘要：
In this paper we consider the inclusion problem involving a maximally monotone operator, a monotone and Lipschitz continuous operator, linear compositions of parallel-sum type monotone operators as well as the normal cone to the set of zeros of another monotone and Lipschitz continuous operator. We propose a forward–backward–forward type algorithm for solving it that assumes an individual evaluation of each operator. Weak ergodic convergence of the sequence of iterates generated by the algorithmic scheme is guaranteed under a condition formulated in terms of the Fitzpatrick function associated to one of the monotone and Lipschitz continuous operators. We also discuss how the proposed penalty scheme can be applied to convex minimization problems and present some numerical experiments in TV-based image inpainting. © 2013, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore.
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页码：451 / 465
页数：14
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