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, 56:3 | Cite as

A new splitting method for monotone inclusions of three operators

  • Yunda Dong
  • Xiaohuan Yu
Article
  • 136 Downloads

Abstract

In this article, we consider monotone inclusions in real Hilbert spaces and suggest a new splitting method. The associated monotone inclusions consist of the sum of one bounded linear monotone operator and one inverse strongly monotone operator and one maximal monotone operator. The new method, at each iteration, first implements one forward–backward step as usual and next implements a descent step, and it can be viewed as a variant of a proximal-descent algorithm in a sense. Its most important feature is that, at each iteration, it needs evaluating the inverse strongly monotone part once only in the forward–backward step and, in contrast, the original proximal-descent algorithm needs evaluating this part twice both in the forward–backward step and in the descent step. Moreover, unlike a recent work, we no longer require the adjoint operation of this bounded linear monotone operator in the descent step. Under standard assumptions, we analyze weak and strong convergence properties of this new method. Rudimentary experiments indicate the superiority of our suggested method over several recently-proposed ones for our test problems.

Keywords

Monotone inclusions Self-adjoint operator Inverse strongly monotone Splitting method Weak convergence 

Mathematics Subject Classification

58E35 65K15 

Notes

Acknowledgements

We are very grateful to Xixian Bai at Shandong University for his help in numerical experiments.

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Copyright information

© Istituto di Informatica e Telematica (IIT) 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsZhengzhou UniversityZhengzhouPeople’s Republic of China

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