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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 65, 2016 - Issue 5
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Articles

A minimization algorithm for equilibrium problems with polyhedral constraints

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Pages 1061-1068 | Received 05 May 2015, Accepted 25 Jul 2015, Published online: 01 Sep 2015

References

  • Blum E, Oettli W. From optimization and variational inequalities to equilibrium problems. Math. Student. 1994;63:123–145.
  • Martinet B. Regularisation d‘inéquations variationelles par approximations successives. RAIRO. 1970;4:154–159.
  • Rockafellar RT. Monotone operators and the proximal point algorithm. SIAM J. Control. Optim. 1976;14:877–898.
  • Moudafi A. Proximal point algorithm extended to equilibrium problem. J. Nat. Geom. 1999;15:91–100.
  • Moudafi A. Proximal methods for a class of bilevel monotone equilibrium problems. J. Global Optim. 2010;47:287–292.
  • Konnov IV. Application of the proximal point method to nonmonotone equilibrium problems. J. Optim. Theory Appl. 2003;119:317–333.
  • Konnov IV, Dyabilkin DA. Nonmonotone equilibrium: coercivity conditions and weak regularization. J. Global Optim. 2011;49:575–587.
  • Nguyen TTV, Strodiot JJ, Nguyen VH. The interior proximal extragradient method for solving equilibrium problems. J. Global Optim. 2009;44:175–192.
  • Tran DQ, Muu LD, Nguyen VH. Extragradient algorithms extended to equilibrium problems. Optimization. 2008;57:749–776.
  • Santos S, Scheimberg S. Inexact subgradient algorithm for equilibrium problems. Comput. Appl. Math. 2011;30:91–107.
  • Mastroeni G. Gap function for equilibrium problems. J. Global Optim. 2004;27:411–426.
  • Yamashita N, Kanzow C, Morimoto T, Fukushima M. An infeasible interior proximal method for convex programming problems with linear constraints. J. Nonlinear Convex Anal. 2001;2:139–156.
  • Burachik RS, Lopes JO, Silva GJP. An inexact interior proximal method for the variational inequality problem. Comput. Appl. Math. 2009;28:1–22.
  • Auslender A, Teboulle M, Ben-Tiba S. Interior proximal and multiplier methods based on second order homogeneous Kernels. Math. Oper. Res. 1999;24:645–668.
  • Auslender A, Teboulle M. Interior gradient and epsilon-subgradient descent methods for constrained convex minimization. Math. Oper. Res. 2004;29:1–26.
  • Rockafellar RT, Wets RJ-B. Variational analysis. Berlin: Springer; 1998.
  • Aussel D, Corvellec JN, Lassonde M. Mean-value property and subdifferential criteria for lower semicontinuous functions. Trans. Am. Math. Soc. 1995;347:4147–4161.
  • Penot J-PT, Quang PH. Generalized convexity of functions and generalized monotonicity of set-valued maps. J. Optim. Theory Appl. 1999;92:343–356.
  • Daniilidis A, Hadjisavvas N, Martinez-Legaz J. An appropriate subdifferential for quasiconvex functions. SIAM J. Optim. 2002;12:407–420.

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