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Application of the Proximal Point Method to a System of Extended Primal-Dual Equilibrium Problems

In: Recent Advances in Optimization

Author

Listed:
  • Igor V. Konnov

    (Kazan University)

Abstract

Summary We consider a general system of equilibrium type problems which can be viewed as an extension of Lagrangean primal-dual equilibrium problems. We propose to solve the system by an inexact proximal point method, which converges to a solution under monotonicity assumptions. In order to make the method implementable, we suggest to make use of a dual descent algorithm and utilize gap functions for ensuring satisfactory accuracy of certain auxiliary problems. Some examples of applications are also given.

Suggested Citation

  • Igor V. Konnov, 2006. "Application of the Proximal Point Method to a System of Extended Primal-Dual Equilibrium Problems," Lecture Notes in Economics and Mathematical Systems, in: Alberto Seeger (ed.), Recent Advances in Optimization, pages 87-102, Springer.
  • Handle: RePEc:spr:lnechp:978-3-540-28258-7_6
    DOI: 10.1007/3-540-28258-0_6
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    Cited by:

    1. I. V. Konnov, 2014. "Right-Hand Side Decomposition for Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 160(1), pages 221-238, January.

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