Convergence results of iterative algorithms for the sum of two monotone operators
 
in reflexive Banach spaces

Tang, Yan; Promkam, Ratthaprom; Cholamjiak, Prasit; Sunthrayuth, Pongsakorn

doi:10.21136/am.2021.0108-20

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2022

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recently, Chang et al [10] proposed a method similar to (1.4) (see [10,Algorithm (11)] for solving Problem (1.3) when A is Bregman inverse strongly monotone and B is maximal monotone. Other recent methods for solving the MIP (1.3), under the same assumptions on A and B in reflexive Banach spaces, can be found in [24,26,27,36,38].…”

Section: Introductionmentioning

confidence: 99%

Convergence of Two Simple Methods for Solving Monotone Inclusion Problems in Reflexive Banach Spaces

2022

View full text Add to dashboard Cite

We propose two very simple methods, the first one with constant step sizes and the second one with self-adaptive step sizes, for finding a zero of the sum of two monotone operators in real reflexive Banach spaces.Our methods require only one evaluation of the single-valued operator at each iteration. Weak convergence results are obtained when the set-valued operator is maximal monotone and the single-valued operator is Lipschitz continuous, and strong convergence results are obtained when either one of these two operators is required, in addition, to be strongly monotone. We also obtain the rate of convergence of our proposed methods in real reflexive Banach spaces. Finally, we apply our results to solving generalized Nash equilibrium problems for gas markets.

show abstract