Forward–backward splitting algorithm for fixed point problems and zeros of the sum of monotone operators

In this paper, we construct a forward–backward splitting algorithm for approximating a zero of the sum of an α -inverse strongly monotone operator and a maximal monotone operator. The strong convergence theorem is then proved under mild conditions. Then, we add a nonexpansive mapping in the algorith...

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Published inArabian Journal of Mathematics Vol. 9; no. 1; pp. 89 - 99
Main Authors Dadashi, Vahid, Postolache, Mihai
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2020
Springer
Springer Nature B.V
Subjects
Algorithms
Computational geometry
Convergence
Convexity
Fixed points (mathematics)
Mapping
Mathematical programming
Mathematics
Mathematics and Statistics
Operators (mathematics)
Splitting
47H09
47H05
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ISSN2193-5343
2193-5351
2193-5351
DOI10.1007/s40065-018-0236-2

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Summary:In this paper, we construct a forward–backward splitting algorithm for approximating a zero of the sum of an α -inverse strongly monotone operator and a maximal monotone operator. The strong convergence theorem is then proved under mild conditions. Then, we add a nonexpansive mapping in the algorithm and prove that the generated sequence converges strongly to a common element of a fixed points set of a nonexpansive mapping and zero points set of the sum of monotone operators. We apply our main result both to equilibrium problems and convex programming.
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ISSN:2193-5343
2193-5351
2193-5351
DOI:10.1007/s40065-018-0236-2