Regularized Penalty Method for General Equilibrium Problems in Banach Spaces

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• 作者：I. V. Konnov (1)
  
  1. Department of System Analysis and Information Technologies ; Kazan Federal University ; ul. Kremlevskaya ; 18 ; Kazan聽 ; 420008 ; Russia
  
• 关键词：Equilibrium problems ; Nonmonotone bi ; functions ; Regularized penalty method ; Coercivity conditions ; Strong convergence ; 90C33 ; 47J20 ; 65K15 ; 65J20
• 刊名：Journal of Optimization Theory and Applications
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：164
• 期：2
• 页码：500-513
• 全文大小：172 KB
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  4. 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)
  5. Muu, L.D., Oettli, W.: A Lagrangian penalty function method for monotone variational inequalities. Numer. Funct. Anal. Optim. 10, 1003鈥?017 (1989) CrossRef
  6. Konnov, I.V.: Regularization method for nonmonotone equilibrium problems. J. Nonlinear Convex Anal. 10, 93鈥?01 (2009)
  7. Konnov, I.V., Dyabilkin, D.A.: Nonmonotone equilibrium problems: coercivity conditions and weak regularization. J. Glob. Optim. 49, 575鈥?87 (2011) CrossRef
  8. Konnov, I.V.: On penalty methods for non monotone equilibrium problems. J. Glob. Optim. 59, 131鈥?38 (2014) CrossRef
  9. Konnov, I.V., Liu, Z.: Vector equilibrium problems on unbounded sets. Lobachevskii J. Math. 31, 232鈥?38 (2010) CrossRef
  10. Ky, Fan: A minimax inequality and applications. In: Shisha, O. (ed.) Inequalities III, pp. 103鈥?13. Academic Press, New York (1972)
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  12. Blum, E., Oettli, W.: From optimization and variational inequalities to equilibrium problems. Math. Stud. 63, 123鈥?45 (1994)
  13. Konnov, I.V.: Combined Relaxation Methods for Variational Inequalities. Springer, Berlin (2001) CrossRef
  14. Konnov, I.V.: Combined relaxation methods for generalized monotone variational inequalities. In: Konnov, I.V., Luc, D.T., Rubinov, A.M. (eds.) Generalized Convexity and Related Topics, pp. 3鈥?1. Springer, Berlin (2007)
  15. Nikaido, H., Isoda, K.: Note on noncooperative convex games. Pac. J. Math. 5, 807鈥?15 (1955) CrossRef
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  19. Bakushinskii, A.B., Goncharskii, A.V.: Iterative Methods for Ill-Posed Problems. Nauka, Moscow (1989) [in Russian]
  20. Konnov, I.V., Ali, M.S.S.: Descent methods for monotone equilibrium problems in Banach spaces. J. Comput. Appl. Math. 188, 165鈥?79 (2006) CrossRef
  21. Konnov, I.V., Ali, M.S.S., Mazurkevich, E.O.: Regularization of nonmonotone variational inequalities. Appl. Math. Optim. 53, 311鈥?30 (2006) CrossRef
  
• 刊物主题：Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operations Research/Decision Theory;
• 出版者：Springer US
• ISSN：1573-2878

文摘

We consider the regularized version of the penalty method for a general equilibrium problem in a Banach space setting. We suggest weak coercivity conditions instead of (generalized) monotonicity and show that they also provide weak and strong convergence properties of the method.