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Right-Hand Side Decomposition for Variational Inequalities

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  • I. V. Konnov

    (Kazan Federal University)

Abstract

We consider a general class of variational inequality problems in a finite-dimensional space setting. The cost mapping need not be the gradient of any function. By using a right-hand side allocation technique, we transform such a problem into a collection of small-dimensional variational inequalities. The master problem is a set-valued variational inequality. We suggest a general iterative method for the problem obtained, which is convergent under monotonicity assumptions. We also show that regularization of partial problems enables us to create single-valued approximations for the cost mapping of the master problem and to propose simpler solution methods.

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  • 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.
    • Handle: RePEc:spr:joptap:v:160:y:2014:i:1:d:10.1007_s10957-013-0370-0
    DOI: 10.1007/s10957-013-0370-0
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    References listed on IDEAS

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    1. Jerzy Kyparisis, 1990. "Sensitivity Analysis for Nonlinear Programs and Variational Inequalities with Nonunique Multipliers," Mathematics of Operations Research, INFORMS, vol. 15(2), pages 286-298, May.
    2. Jerzy Kyparisis, 1992. "Parametric Variational Inequalities with Multivalued Solution Sets," Mathematics of Operations Research, INFORMS, vol. 17(2), pages 341-364, May.
    3. Igor V. Konnov, 2007. "Combined Relaxation Methods for Generalized Monotone Variational Inequalities," Lecture Notes in Economics and Mathematical Systems, in: Generalized Convexity and Related Topics, pages 3-31, Springer.
    4. 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.
    5. Fuller, J. David & Chung, William, 2008. "Benders decomposition for a class of variational inequalities," European Journal of Operational Research, Elsevier, vol. 185(1), pages 76-91, February.
    6. I. V. Konnov & S. Schaible & J. C. Yao, 2005. "Combined Relaxation Method for Mixed Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 126(2), pages 309-322, August.
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    1. E. Allevi & A. Gnudi & I. V. Konnov & G. Oggioni, 2018. "Decomposition method for oligopolistic competitive models with common environmental regulation," Annals of Operations Research, Springer, vol. 268(1), pages 441-467, September.

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