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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Vydané v:	Arabian Journal of Mathematics Ročník 9; číslo 1; s. 89 - 99
Hlavní autori:	Dadashi, Vahid, Postolache, Mihai
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2020 Springer Springer Nature B.V
Predmet:	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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Abstract	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.
AbstractList	In this paper, we construct a forward-backward splitting algorithm for approximating a zero of the sum of an [alpha]-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. In this paper, we construct a forward-backward splitting algorithm for approximating a zero of the sum of an [alpha]-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. Mathematics Subject Classification 47H05 * 47H09 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. 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.
Audience	Academic
Author	Postolache, Mihai Dadashi, Vahid
Author_xml	– sequence: 1 givenname: Vahid surname: Dadashi fullname: Dadashi, Vahid organization: Department of Mathematics, Sari Branch, Islamic Azad University – sequence: 2 givenname: Mihai surname: Postolache fullname: Postolache, Mihai email: mihai@mathem.pub.ro organization: China Medical University, Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, Department of Mathematics and Computer Science, University Politehnica of Bucharest
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Snippet	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... In this paper, we construct a forward-backward splitting algorithm for approximating a zero of the sum of an [alpha]-inverse strongly monotone operator and a... 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...
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SubjectTerms	Algorithms Computational geometry Convergence Convexity Fixed points (mathematics) Mapping Mathematical programming Mathematics Mathematics and Statistics Operators (mathematics) Splitting
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Title	Forward–backward splitting algorithm for fixed point problems and zeros of the sum of monotone operators
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