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A New Two-Step Proximal Algorithm of Solving the Problem of Equilibrium Programming

In: Optimization and Its Applications in Control and Data Sciences

Author

Listed:
  • Sergey I. Lyashko

    (Kiev National Taras Shevchenko University)

  • Vladimir V. Semenov

    (Kiev National Taras Shevchenko University)

Abstract

We propose a new iterative two-step proximal algorithm for solving the problem of equilibrium programming in a Hilbert space. This method is a result of extension of L.D. Popov’s modification of Arrow-Hurwicz scheme for approximation of saddle points of convex-concave functions. The convergence of the algorithm is proved under the assumption that the solution exists and the bifunction is pseudo-monotone and Lipschitz-type.

Suggested Citation

  • Sergey I. Lyashko & Vladimir V. Semenov, 2016. "A New Two-Step Proximal Algorithm of Solving the Problem of Equilibrium Programming," Springer Optimization and Its Applications, in: Boris Goldengorin (ed.), Optimization and Its Applications in Control and Data Sciences, pages 315-325, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-42056-1_10
    DOI: 10.1007/978-3-319-42056-1_10
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    Citations

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    Cited by:

    1. Pasakorn Yordsorn & Poom Kumam & Habib ur Rehman & Abdulkarim Hassan Ibrahim, 2020. "A Weak Convergence Self-Adaptive Method for Solving Pseudomonotone Equilibrium Problems in a Real Hilbert Space," Mathematics, MDPI, vol. 8(7), pages 1-24, July.
    2. Habib ur Rehman & Poom Kumam & Ioannis K. Argyros & Meshal Shutaywi & Zahir Shah, 2020. "Optimization Based Methods for Solving the Equilibrium Problems with Applications in Variational Inequality Problems and Solution of Nash Equilibrium Models," Mathematics, MDPI, vol. 8(5), pages 1-28, May.
    3. Yekini Shehu & Olaniyi S. Iyiola & Duong Viet Thong & Nguyen Thi Cam Van, 2021. "An inertial subgradient extragradient algorithm extended to pseudomonotone equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(2), pages 213-242, April.
    4. Lateef Olakunle Jolaoso & Christian Chibueze Okeke & Yekini Shehu, 2021. "Extragradient Algorithm for Solving Pseudomonotone Equilibrium Problem with Bregman Distance in Reflexive Banach Spaces," Networks and Spatial Economics, Springer, vol. 21(4), pages 873-903, December.
    5. Habib ur Rehman & Poom Kumam & Meshal Shutaywi & Nasser Aedh Alreshidi & Wiyada Kumam, 2020. "Inertial Optimization Based Two-Step Methods for Solving Equilibrium Problems with Applications in Variational Inequality Problems and Growth Control Equilibrium Models," Energies, MDPI, vol. 13(12), pages 1-28, June.

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