A proximal augmented Lagrangian method for equilibrium problems

References

• Antipin , AS . 1997 . Equilibrium programming: Proximal methods . Comput. Math. Math. Phys. , 37 : 1285 – 1296 .
   Google Scholar
• Antipin , AS , Vasilev , FP and Stukalov , AS . 2007 . A regularized Newton method for solving equilibrium programming problems with an inexactly specified set . Comput. Math. Math. Phys. , 47 : 19 – 31 .
   Google Scholar
• Auslender , A and Teboulle , M . 2000 . Lagrangian duality and related multiplier methods for variational inequality problems . SIAM J. Optim. , 10 : 1097 – 1115 .
   Web of Science ®Google Scholar
• Flåm , SD and Antipin , AS . 1997 . Equilibrium programming using proximal-like algorithms . Math. Program. , 78 : 29 – 41 .
   Web of Science ®Google Scholar
• Iusem , AN and Nasri , M . 2010 . Augmented Lagrangian methods for variatinal inequality problems . RAIRO-Oper. Res. , 44 : 5 – 25 .
   Web of Science ®Google Scholar
• Iusem , AN and Nasri , M . 2007 . Inexact proximal point methods for equilibrium problems in Banach spaces . Numer. Funct. Anal. Optim. , 28 : 1279 – 1308 .
   Web of Science ®Google Scholar
• Iusem , AN and Sosa , W . 2010 . On the proximal point method for equilibrium problems in Hilbert spaces . Optimization , 59 : 1259 – 1274 .
   Web of Science ®Google Scholar
• Konnov , IV . 2003 . Application of the proximal point method to nonmonotone equilibrium problems . J. Optim. Theory Appl. , 119 : 317 – 333 .
   Web of Science ®Google Scholar
• Moudafi , A . 1999 . Proximal point methods extended to equilibrium problems . J. Natural Geom. , 15 : 91 – 100 .
   Google Scholar
• Moudafi , A . 2003 . Second-order differential proximal methods for equilibrium problems . J. Inequalities Pure Appl. Math. , 4 Article no. 18
   Google Scholar
• Moudafi , A and Thêra , M . 1999 . “ Proximal and dynamical approaches to equilibrium problems ” . In Illposed Variational Problems and Regularization Techniques, Lecture Notes in Economics and Mathematical Systems , Vol. 477 , 187 – 201 . Berlin : Springer .
   Google Scholar
• Muu , LD and Oettli , W . 1992 . Convergence of an adaptive penalty scheme for finding constraint equilibria . Nonlinear Anal. , 18 : 1159 – 1166 .
   Web of Science ®Google Scholar
• Noor , MA . 2004 . Auxiliary principle technique for equilibrium problems . J. Optim. Theory Appl. , 122 : 371 – 386 .
   Web of Science ®Google Scholar
• Noor , MA and Rassias , TM . 2005 . On nonconvex equilibrium problems . J. Math. Anal. Appl. , 212 : 289 – 299 .
   Web of Science ®Google Scholar
• Bertsekas , DP . 1976 . On penalty and multiplier methods for constrained optimization problems . SIAM J. Control Optim. , 14 : 216 – 235 .
   Web of Science ®Google Scholar
• Hestenes , MR . 1969 . Multiplier and gradient methods . J. Optim. Theory Appl. , 4 : 303 – 320 .
   Google Scholar
• Powell , MJD . 1969 . “ Method for nonlinear constraints in minimization problems ” . In Optimization , Edited by: Fletcher , R . London : Academic Press .
   Google Scholar
• Rockafellar , RT . 1976 . Augmented Lagrangians and applications of the proximal point algorithm in convex programming . Math. Oper. Res. , 1 : 97 – 116 .
   Google Scholar
• Rockafellar , RT . 1973 . The multiplier method of Hestenes and Powell applied to convex programming . J. Optim. Theory Appl. , 12 : 555 – 562 .
   Web of Science ®Google Scholar
• Butnariu , D and Iusem , AN . 2000 . Totally Convex Functions for Fixed Points Computation and Infinite-dimensional Optimization , Dordrecht : Kluwer .
   Google Scholar
• Iusem , AN and Gârciga Otero , R . 2002 . Augmented Lagrangian methods for cone-constrained convex optimization in Banach spaces . J. Nonlinear Convex Anal. , 3 : 155 – 176 .
   Google Scholar
• Wierzbicki , AP and Kurcyusz , S . 1977 . Projection on a cone, penalty functionals and duality theory for problems with inequaltity constraints in Hilbert space . SIAM J. Control Optim. , 15 : 25 – 56 .
   Web of Science ®Google Scholar
• Iusem , AN and Gârciga Otero , R . 2001 . Inexact versions of proximal point and augmented Lagrangian algorithms in Banach spaces . Numer. Funct. Anal. Optim. , 22 : 609 – 640 .
   Web of Science ®Google Scholar
• Mashreghi , J and Nasri , M . 2010 . Strong convergence of an inexact proximal point method for equilibrium problems in Banach spaces . Numer. Funct. Anal. Optim. , 31 : 1053 – 1071 .
   Web of Science ®Google Scholar
• Luenberger , DG . 1969 . Optimization by vector space methods , New york : John Wiley & Sons .
   Google Scholar
• Cioranescu , I . 1990 . Geometry of Banach Spaces, Duality Mappings, and Nonlinear Problems , Dordrecht : Kluwe Academic Publishers Group .
   Google Scholar
• Penot , JP and Ratsimahalo , R . 1998 . Characterization of metric projections in Banach spaces and applications . Abstract Appl. Anal. , 3 : 85 – 103 .
   Google Scholar
• Breton , M , Zaccour , G and Zahaf , M . 2005 . A differential game of joint implementation of environmental projects . Automatica , 41 : 1737 – 1749 .
   Web of Science ®Google Scholar
• Iusem , AN and Nasri , M . Korpelevich's method for variational inequality problems in Banach spaces . J. Global Optim. , DOI: 10.1007/s10898-010-9613-x (in press)
   Google Scholar
• Mashreghi , J and Nasri , M . 2010 . Forcing strong convergence of Korpelevich's method in Banach spaces with its applications in game theory . Nonlinear Anal. , 72 : 2086 – 2099 .
   Web of Science ®Google Scholar