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Merit functions: a bridge between optimization and equilibria

Author

Listed:
  • Massimo Pappalardo

    (Università di Pisa)

  • Giandomenico Mastroeni

    (Università di Pisa)

  • Mauro Passacantando

    (Università di Pisa)

Abstract

In the last decades, many problems involving equilibria, arising from engineering, physics and economics, have been formulated as variational mathematical models. In turn, these models can be reformulated as optimization problems through merit functions. This paper aims at reviewing the literature about merit functions for variational inequalities, quasi-variational inequalities and abstract equilibrium problems. Smoothness and convexity properties of merit functions and solution methods based on them will be presented.

Suggested Citation

  • Massimo Pappalardo & Giandomenico Mastroeni & Mauro Passacantando, 2016. "Merit functions: a bridge between optimization and equilibria," Annals of Operations Research, Springer, vol. 240(1), pages 271-299, May.
    • Handle: RePEc:spr:annopr:v:240:y:2016:i:1:d:10.1007_s10479-015-2013-3
    DOI: 10.1007/s10479-015-2013-3
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    1. Anna Nagurney, 2010. "Formulation and analysis of horizontal mergers among oligopolistic firms with insights into the merger paradox: a supply chain network perspective," Computational Management Science, Springer, vol. 7(4), pages 377-406, October.
    2. Zhao, Lan & Nagurney, Anna, 2008. "A network equilibrium framework for Internet advertising: Models, qualitative analysis, and algorithms," European Journal of Operational Research, Elsevier, vol. 187(2), pages 456-472, June.
    3. Giancarlo Bigi & Mauro Passacantando, 2015. "D-gap functions and descent techniques for solving equilibrium problems," Journal of Global Optimization, Springer, vol. 62(1), pages 183-203, May.
    4. Stella Dafermos, 1980. "Traffic Equilibrium and Variational Inequalities," Transportation Science, INFORMS, vol. 14(1), pages 42-54, February.
    5. Bigi, Giancarlo & Castellani, Marco & Pappalardo, Massimo & Passacantando, Mauro, 2013. "Existence and solution methods for equilibria," European Journal of Operational Research, Elsevier, vol. 227(1), pages 1-11.
    6. Forgo, Ferenc & Fulop, Janos & Prill, Maria, 2005. "Game theoretic models for climate change negotiations," European Journal of Operational Research, Elsevier, vol. 160(1), pages 252-267, January.
    7. Miller, Naomi & Ruszczynski, Andrzej, 2008. "Risk-adjusted probability measures in portfolio optimization with coherent measures of risk," European Journal of Operational Research, Elsevier, vol. 191(1), pages 193-206, November.
    8. Barbara Panicucci & Massimo Pappalardo & Mauro Passacantando, 2009. "A globally convergent descent method for nonsmooth variational inequalities," Computational Optimization and Applications, Springer, vol. 43(2), pages 197-211, June.
    9. Tran Quoc & Le Muu, 2012. "Iterative methods for solving monotone equilibrium problems via dual gap functions," Computational Optimization and Applications, Springer, vol. 51(2), pages 709-728, March.
    10. Sang Nguyen & Clermont Dupuis, 1984. "An Efficient Method for Computing Traffic Equilibria in Networks with Asymmetric Transportation Costs," Transportation Science, INFORMS, vol. 18(2), pages 185-202, May.
    11. B. Qu & C. Y. Wang & J. Z. Zhang, 2003. "Convergence and Error Bound of a Method for Solving Variational Inequality Problems via the Generalized D-Gap Function," Journal of Optimization Theory and Applications, Springer, vol. 119(3), pages 535-552, December.
    12. L.R. Huang & K. F. Ng, 2005. "Equivalent Optimization Formulations and Error Bounds for Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 125(2), pages 299-314, May.
    13. Lkhamsuren Altangerel & Radu Ioan Boţ & Gert Wanka, 2007. "On The Construction Of Gap Functions For Variational Inequalities Via Conjugate Duality," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 24(03), pages 353-371.
    14. D. Aussel & R. Correa & M. Marechal, 2011. "Gap Functions for Quasivariational Inequalities and Generalized Nash Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 151(3), pages 474-488, December.
    15. Rachana Gupta & Aparna Mehra, 2012. "Gap functions and error bounds for quasi variational inequalities," Journal of Global Optimization, Springer, vol. 53(4), pages 737-748, August.
    16. Zugang Liu & Anna Nagurney, 2007. "Financial Networks with Intermediation and Transportation Network Equilibria: A Supernetwork Equivalence and Reinterpretation of the Equilibrium Conditions with Computations," Computational Management Science, Springer, vol. 4(3), pages 243-281, July.
    17. Giancarlo Bigi & Mauro Passacantando, 2012. "Gap functions and penalization for solving equilibrium problems with nonlinear constraints," Computational Optimization and Applications, Springer, vol. 53(2), pages 323-346, October.
    18. Francisco Facchinei & Christian Kanzow, 2010. "Generalized Nash Equilibrium Problems," Annals of Operations Research, Springer, vol. 175(1), pages 177-211, March.
    19. M. Pappalardo & M. Passacantando, 2002. "Stability for Equilibrium Problems: From Variational Inequalities to Dynamical Systems," Journal of Optimization Theory and Applications, Springer, vol. 113(3), pages 567-582, June.
    20. Laurent Drouet & Alain Haurie & Francesco Moresino & Jean-Philippe Vial & Marc Vielle & Laurent Viguier, 2008. "An oracle based method to compute a coupled equilibrium in a model of international climate policy," Computational Management Science, Springer, vol. 5(1), pages 119-140, February.
    21. E. Cavazzuti & M. Pappalardo & M. Passacantando, 2002. "Nash Equilibria, Variational Inequalities, and Dynamical Systems," Journal of Optimization Theory and Applications, Springer, vol. 114(3), pages 491-506, September.
    22. N. Yamashita & K. Taji & M. Fukushima, 1997. "Unconstrained Optimization Reformulations of Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 92(3), pages 439-456, March.
    23. D. Chan & J. S. Pang, 1982. "The Generalized Quasi-Variational Inequality Problem," Mathematics of Operations Research, INFORMS, vol. 7(2), pages 211-222, May.
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