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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 62, 2013 - Issue 2
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Articles

A note on D-gap functions for equilibrium problems

Pages 211-226 | Received 19 Sep 2009, Accepted 14 Apr 2011, Published online: 30 Jun 2011

References

  • Ansari , QH and Yao , JC . 1999 . Generalised variational-like inequalities and a gap function . Bull. Aus. Math. Soc. , 59 : 33 – 44 .
  • Auchmuty , G . 1989 . Variational principles for variational inequalities . Numer. Funct. Anal. Optim. , 10 : 863 – 874 .
  • Auslender , A . 1976 . Optimization: Methodes Numeriques (livre) , Paris : Masson .
  • Bank , B , Guddat , J , Klatte , D , Kummer , B and Tammer , K . 1983 . Nonlinear Parametric Optimization , Basel : Birkhauser Verlag .
  • Browder , FE . 1966 . Existence and approximation of solutions of nonlinear variational inequalities . Proc. Nat. Acad. Aci. U.S.A. , 56 : 1080 – 1086 .
  • Chadli , O , Konnov , IV and Yao , JC . 2004 . Descent methods for equilibrium problems in a Banach space . Comp. Math. Appl. , 48 : 609 – 616 .
  • Chadli , O , Liu , ZH and Yao , JC . 2007 . Applications of equilibrium problems to a class of noncoercive variational inequalities . J. Optim. Theory Appl. , 132 : 89 – 110 .
  • Chadli , O , Schaible , S and Yao , JC . 2004 . Regularized equilibrium problems with an application to noncoercive hemivariational inequalities . J. Optim. Theory Appl. , 121 : 571 – 596 .
  • Fukushima , M . 1992 . Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems . Math. Prog. , 53 : 99 – 110 .
  • Guo , JS and Yao , JC . 1994 . Variational inequalities with nonmonotone operators . J. Optim. Theory Appl. , 80 : 63 – 74 .
  • Konnov , IV and Pinyagina , OV . 2003 . D-gap functions for a class of equilibrium problems in Banach spaces . Comput. Methods Appl. Math. , 3 : 274 – 286 .
  • Konnov , IV , Schaible , S and Yao , JC . 2005 . Combined relaxation method mixed equilibrium problems . J. Opt. Theory Appl. , 126 : 309 – 322 .
  • Lescarret , C . 1965 . ‘cas d’ addition des applications monotones maximales dans espaces de Hilbert . Compt. Rend. Sci. (Paris). , 261 : 1160 – 1163 .
  • Mastroeni , G . 2003 . Gap functions for equilibrium problems . J. Global Optim. , 27 : 411 – 426 .
  • Pang , JS and Yao , JC . 1994 . On the generalizaton of a normal map and equation . SIAM J. Control optim. , 33 : 168 – 184 .
  • Peng , JM . 1997 . Equivalence of variational inequality problems to unconstrained minimization . Math. Prog. , 78 : 347 – 355 .
  • Peng , JW and Yao , JC . 2008 . A hybrid-extragradient method for generalized mixed equilibrium problems fixed point problems and variational inequaity problems . Taiwanese J. Math. , 12 : 1401 – 1433 .
  • Solodov , MV . 2003 . Merit functions and eroor bounds for generalized variational inequalities . J. Math. Anal. Appl. , 287 : 405 – 414 .
  • Wu , JH , Florian , M and Marcotte , P . 1993 . A general descent framework for the monotone variational inequality problem . Math. Prog. , 61 : 281 – 300 .
  • Yamashita , N , Taji , K and Fukushima , M . 1997 . Unconstrained optimization reformulations of variational inequality problems . J. Optim. Theory Appl. , 92 : 439 – 456 .
  • Yao , JC and Chadli , O . 2005 . “ Pseudomonotone complementarity problems and variational inequalities ” . In Handbook of Generalized Convexity and Monotonicity , Edited by: Crouzeix , JP , Haddjissas , N and Schaible , S . 501 – 558 . New York : Springer .
  • Zeng , LC , Wu , SY and Yao , JC . 2006 . Generalized KKM Theorem with Applications to Generalized Minimax inequalities and generalized equilibrium problems . Taiwanese J. Math. , 10 : 1497 – 1514 .
  • Zeng , LC and Yao , JC . 2006 . Modified combined relaxation method for general monotone equilibrium problems in Hilbert spaces . J. Opt. Theory Appl. Comput. , 131 : 469 – 483 .
  • Zeng , LC and Yao , JC . 2008 . A hybrid iterative scheme for mixed equilibrium problems and fixed point problems . J. Comp. Appl. Math. Comput. , 214 : 186 – 201 .
  • Zeng , LC and Yao , JC . 2008 . Hybrid viscosity approximation schemes for equilibrium problems and fixed point problemsof infinitely many nonexpansive mappings . Appl. Math. Comput. , 198 : 729 – 741 .
  • Zhang , LP and Han , JY . 2009 . Unconstrained optimization reformulations of equilibrium problems . Acta Math. Sin. (Eng Ser.) , 25 : 343 – 354 .
  • Zhang , LP and Wu , SY . 2009 . An algorithm based on the generalized D-gap function for equilibrium problems . J. Comput. Appl. Math. , 231 : 403 – 411 .
  • Zhu , DL and Marcotte , P . 1994 . An extended descent frameowrk for variational inequalities . J. Opt. Theory Appl. , 80 : 349 – 366 .

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