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An inertial-like proximal algorithm for equilibrium problems

MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2018年第3期88卷 399-415页

作者： Van Hieu, Dang Ton Duc Thang Univ Fac Math & Stat Appl Anal Res Grp Ho Chi Minh City Vietnam

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.

关键词： Proximal point algorithm inertial-like algorithm Monotone bifunction

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Strong convergence of inertial algorithms for solving equilibrium problems

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OPTIMIZATION LETTERS 2020年第7期14卷 1817-1843页

作者： Van Hieu, Dang Gibali, Aviv Ton Duc Thang Univ Fac Math & Stat Appl Anal Res Grp Ho Chi Minh City Vietnam ORT Braude Coll Dept Math IL-2161002 Karmiel Israel Univ Haifa Ctr Math & Sci Computat IL-3498838 Haifa Israel

In this paper, we introduce several inertial-like algorithms for solving equilibrium problems (EP) in real Hilbert spaces. The algorithms are constructed using the resolvent of the EP associated bifunction and combines the inertial and the Mann-type technique. Under mild and standard conditions imposed on the cost bifunction and control parameters strong convergence of the algorithms is established. We present several numerical examples to illustrate the behavior of our schemes and emphasize their convergence advantages compared with some related methods.

关键词： Proximal point algorithm inertial-like algorithm Monotone bifunction

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