On penalty methods for non monotone equilibrium problems

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• 作者：I. V. Konnov (1)
  
• 关键词：Equilibrium problems ; Nonmonotone bifunctions ; Penalty method ; Coercivity conditions ; Regularized penalty method ; 90C33 ; 47J20 ; 65K15 ; 65J20
• 刊名：Journal of Global Optimization
• 出版年：2014
• 出版时间：May 2014
• 年：2014
• 卷：59
• 期：1
• 页码：131-138
• 全文大小：140 KB
• 参考文献：1. Baiocchi, C., Capelo, A.: Variational and Quasivariational Inequalities: Applications to Free Boundary Problems. Wiley, New York (1984)
  2. Blum, E., Oettli, W.: From optimization and variational inequalities to equilibrium problems. Math. Stud. 63, 123鈥?45 (1994)
  3. Konnov, I.V.: Combined Relaxation Methods for Variational Inequalities. Springer, Berlin (2001) CrossRef
  4. Konnov, I.V.: Generalized monotone equilibrium problems and variational inequalities. In: Hadjisavvas, N., Koml贸si, S., Schaible, S. (eds.) Handbook of Generalized Convexity and Generalized Monotonicity, 鈥淣onconvex Optimization and Applications鈥? vol. 76, pp. 559鈥?18. Springer, New York (2005) CrossRef
  5. Gwinner, J.: On the penalty method for constrained variational inequalities. In: Hiriart-Urruty, J.-B., Oettli, W., Stoer, J. (eds.) Optimization: Theory and Algorithms, pp. 197鈥?11. Marcel Dekker, New York (1981)
  6. Muu, L.D., Oettli, W.: A Lagrangian penalty function method for monotone variational inequalities. Numer. Funct. Anal. Optim. 10, 1003鈥?017 (1989) CrossRef
  7. Antipin, A.S., Vasil鈥檈v, F.P.: A stabilization method for equilibrium programming problems with an approximately given set. Comput. Math. Math. Phys. 39, 1707鈥?714 (1999)
  8. Konnov, I.V.: Regularization method for nonmonotone equilibrium problems. J. Nonlin. Convex Anal. 10, 93鈥?01 (2009)
  9. Konnov, I.V., Dyabilkin, D.A.: Nonmonotone equilibrium problems: coercivity conditions and weak regularization. J. Glob. Optim. 49, 575鈥?87 (2011) CrossRef
  10. Fan, K.: A minimax inequality and applications. In: Shisha, O. (ed.) Inequalities III, pp. 103鈥?13. Academic Press, New York (1972)
  11. Bianchi, M., Pini, R.: Coercivity conditions for equilibrium problems. J. Optim. Theory Appl. 124, 79鈥?2 (2005) CrossRef
  12. Sukharev, A.G., Timokhov, A.V., Fedorov, V.V.: A Course in Optimization Methods. Nauka, Moscow (1986). (in Russian)
  13. Bianchi, M., Hadjisavvas, N., Schaible, S.: Minimal coercivity conditions and exceptional families of elements in quasimonotone variational inequalities. J. Optim. Theory Appl. 122, 1鈥?7 (2004)
  14. Nikaido, H., Isoda, K.: Note on noncooperative convex games. Pac. J. Math. 5, 807鈥?15 (1955) CrossRef
  15. Rosen, J.B.: Existence and uniqueness of equilibrium points for concave $n$ -person games. Econometrica 33, 520鈥?34 (1965) CrossRef
  16. Facchinei, F., Kanzow, C.: Penalty methods for the solution of generalized Nash equilibrium problems. SIAM J. Optim. 20, 2228鈥?253 (2010) CrossRef
  17. Konnov, I.V.: Spatial equilibrium problems for auction type systems. Russ. Math. (Iz. VUZ) 52(1), 30鈥?4 (2008)
  18. Konnov, I.V.: Decomposition approaches for constrained spatial auction market problems. Netw. Sp. Econ. 9, 505鈥?24 (2009) CrossRef
  
• 作者单位：I. V. Konnov (1)
  
  1. Department of System Analysis and Information Technologies, Kazan Federal University, ul. Kremlevskaya, 18, 420008, Kazan, Russia
  
• ISSN：1573-2916

文摘

We consider a general equilibrium problem under weak coercivity conditions in a finite-dimensional space setting. It appears such a condition provides convergence of the general penalty method without any monotonicity assumptions. We also show that the regularized version of the penalty method enables us to further weaken the coercivity condition.