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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Vydáno v:Arabian Journal of Mathematics Ročník 9; číslo 1; s. 89 - 99
Hlavní autoři: Dadashi, Vahid, Postolache, Mihai
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2020
Springer
Springer Nature B.V
Témata:
Algorithms
Computational geometry
Convergence
Convexity
Fixed points (mathematics)
Mapping
Mathematical programming
Mathematics
Mathematics and Statistics
Operators (mathematics)
Splitting
47H09
47H05
ISSN:2193-5343, 2193-5351, 2193-5351
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Popis
Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:2193-5343
2193-5351
2193-5351
DOI:10.1007/s40065-018-0236-2