Regularized gradient-projection methods for the constrained convex minimization problem and the zero points of maximal monotone operator

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• 作者：Ming Tian (1) (2)
  Si-Wen Jiao (1)
  
  1. College of Science ; Civil Aviation University of China ; Tianjin ; 300300 ; China
  2. Tianjin Key Laboratory for Advanced Signal Processing ; Civil Aviation University of China ; Tianjin ; 300300 ; China
  
• 关键词：58E35 ; 47H09 ; 65J15 ; iterative method ; fixed point ; constrained convex minimization ; maximal monotone operator ; resolvent ; equilibrium problem ; variational inequality
• 刊名：Fixed Point Theory and Applications
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：2015
• 期：1
• 全文大小：1,302 KB
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• 刊物主题：Analysis; Mathematics, general; Applications of Mathematics; Differential Geometry; Topology; Mathematical and Computational Biology;
• 出版者：Springer International Publishing
• ISSN：1687-1812

文摘

In this paper, based on the viscosity approximation method and the regularized gradient-projection algorithm, we find a common element of the solution set of a constrained convex minimization problem and the set of zero points of the maximal monotone operator problem. In particular, the set of zero points of the maximal monotone operator problem can be transformed into the equilibrium problem. Under suitable conditions, new strong convergence theorems are obtained, which are useful in nonlinear analysis and optimization. As an application, we apply our algorithm to solving the split feasibility problem and the constrained convex minimization problem in Hilbert spaces.