Backward Penalty Schemes for Monotone Inclusion Problems

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• 作者：Sebastian Banert ; Radu Ioan Bo?
• 关键词：Backward penalty algorithm ; Monotone inclusion ; Maximally monotone operator ; Fitzpatrick function ; Convex subdifferential ; 47H05 ; 65K05 ; 90C25
• 刊名：Journal of Optimization Theory and Applications
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：166
• 期：3
• 页码：930-948
• 全文大小：506 KB
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• 作者单位：Sebastian Banert (1)
  Radu Ioan Bo? (1)
  
  1. University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Vienna, Austria
  
• 刊物主题：Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operations Research/Decision Theory;
• 出版者：Springer US
• ISSN：1573-2878

文摘

In this paper, we are concerned with solving monotone inclusion problems expressed by the sum of a set-valued maximally monotone operator with a single-valued maximally monotone one and the normal cone to the nonempty set of zeros of another set-valued maximally monotone operator. Depending on the nature of the single-valued operator, we propose two iterative penalty schemes, both addressing the set-valued operators via backward steps. The single-valued operator is evaluated via a single forward step if it is cocoercive, and via two forward steps if it is monotone and Lipschitz continuous. The latter situation represents the starting point for dealing with complexly structured monotone inclusion problems from algorithmic point of view.