An inertial-like proximal algorithm for equilibrium problems

The paper concerns with an inertial-like algorithm for approximating solutions of equilibrium problems in Hilbert spaces. The algorithm is a combination around the relaxed proximal point method, inertial effect and the Krasnoselski–Mann iteration. The using of the proximal point method with relaxati...

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Bibliographic Details
Published in:Mathematical methods of operations research (Heidelberg, Germany) Vol. 88; no. 3; pp. 399 - 415
Main Author: Van Hieu, Dang
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2018
Springer Nature B.V
Subjects:
Algorithms
Business and Management
Calculus of Variations and Optimal Control; Optimization
Convergence
Goal programming
Hilbert space
Iterative methods
Mathematics
Mathematics and Statistics
Operations research
Operations Research/Decision Theory
Original Article
Monotone bifunction
47J20
Proximal point algorithm
47H05
47J25
65J15
Inertial-like algorithm
91B50
ISSN:1432-2994, 1432-5217
Online Access:Get full text
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Summary:The paper concerns with an inertial-like algorithm for approximating solutions of equilibrium problems in Hilbert spaces. The algorithm is a combination around the relaxed proximal point method, inertial effect and the Krasnoselski–Mann iteration. The using of the proximal point method with relaxations has allowed us a more flexibility in practical computations. The inertial extrapolation term incorporated in the resulting algorithm is intended to speed up convergence properties. The main convergence result is established under mild conditions imposed on bifunctions and control parameters. Several numerical examples are implemented to support the established convergence result and also to show the computational advantage of our proposed algorithm over other well known algorithms.
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ISSN:1432-2994
1432-5217
DOI:10.1007/s00186-018-0640-6