Publication Cover
Optimization
A Journal of Mathematical Programming and Operations Research
Volume 62, 2013 - Issue 9
163
Views
4
CrossRef citations to date
0
Altmetric
Articles

Interior proximal methods for equilibrium programming: part I

Pages 1247-1266 | Received 11 Aug 2010, Accepted 11 Sep 2011, Published online: 02 Dec 2011

References

  • Bauschke , HH and Borwein , JM . 1997 . Legendre functions and the method of random Bregman projections . J. Convex Anal. , 4 : 27 – 67 .
  • Bigi , G , Castellani , M and Pappalardo , M . 2009 . A new solution method for equilibrium problems . Optim. Methods Softw. , 24 : 895 – 911 .
  • Blum , E and Oettli , W . 1994 . From optimization and variational inequalities to equilibrium problems . Math. Stud. , 63 : 123 – 145 .
  • Burachik , RS and Iusem , AN . 1998 . A generalized proximal point algorithm for the variational inequality problem in Hilbert space . SIAM J. Optim. , 8 : 197 – 216 .
  • Cavazutti , E , Pappalardo , M and Passacantando , M . 2002 . Nash equilibria, variational inequalities and dynamical systems . J. Optim. Theory Appl. , 114 : 491 – 506 .
  • Censor , Y , Iusem , AN and Zenios , SA . 1998 . An interior point method with Bregman functions for the variational inequality problem with paramonotone operators . Math. Program. , 81 : 373 – 400 .
  • Censor , Y and Zenios , SA . 1992 . Proximal minimization algorithm with D-functions . J. Optim. Theory Appl. , 73 : 451 – 464 .
  • Chen , G and Teboulle , M . 1993 . Convergence analysis of a proximal like minimization algorithm using Bregman functions . SIAM J. Optim. , 3 : 538 – 543 .
  • Crouzeix , J-P , Marcotte , P and Zhu , D . 2000 . Conditions ensuring the applicability of cutting plane methods for solving variational inequalities . Math. Program. , 88 : 521 – 539 .
  • Eckstein , J . 1993 . Nonlinear proximal point algorithms using Bregman functions, with application to convex programming . Math. Oper. Res. , 18 : 202 – 226 .
  • Facchinei , F and Kanzow , C . 2007 . Generalized Nash equilibrium problems . 4 OR , 5 : 173 – 210 .
  • Facchinei , F and Pang , J-S . 2003 . Finite-Dimensional Variational Inequalities and Complementarity Problems , New York, Berlin, Heidelberg, Hong Kong, London, Milan, Paris, Tokyo : Springer .
  • Flåm , SD and Antipin , AS . 1997 . Equilibrium programming using proximal-like algorithms . Math. Program. , 77 : 29 – 41 .
  • Flåm , SD and Ruszczynski , A . 2008 . Finding normalized equilibrium in convex-concave games . Int. Game Theory Rev. , 10 : 37 – 58 .
  • Hiriart-Urruty , J-B and Lemarechal , C . 1993 . Convex Analysis and Minimization Algorithms , Berlin : Springer Verlag .
  • Iusem , AN . 2011 . On the maximal monotonicity of diagonal subdifferential operators . J. Convex Anal. , 18 : 489 – 503 .
  • Iusem , AN , Kassay , G and Sosa , W . 2009 . On certain conditions for the existence of solutions of equilibrium problems . Math. Program. B , 116 : 259 – 273 .
  • Iusem , AN and Nasri , M . 2007 . Inexact proximal point methods for equilibrium problems in Banach spaces . Numer. Funct. Anal. Optim. , 28 : 1279 – 1308 .
  • Iusem , AN and Sosa , W . 2010 . On the proximal point method for equilibrium problems in Hilbert spaces . Optimization , 59 : 1259 – 1274 .
  • Kaplan , A and Tichatschke , R . 2010 . Note on the paper: Interior proximal method for variational inequalities on non-polyhedral sets . Discus. Math.: Differ. Inclusions, Control Optim. , 30 : 51 – 59 .
  • Langenberg , N . Interior proximal methods for equilibrium programming: Part II, Optimization , (to appear). doi: 10.1080/02331934.2011.627334
  • Langenberg , N . 2010 . Pseudomonotone operators and the Bregman proximal point algorithm . J. Global Optim. , 47 : 537 – 555 .
  • Langenberg , N . 2011 . Convergence analysis of an extended Auxiliary Problem Principle with various stopping criteria . Optim. Methods Softw. , 26 : 127 – 154 .
  • Langenberg , N . 2011 . On the cutting plane property and the Bregman Proximal Point Algorithm . J. Convex Anal. , 18 : 601 – 619 .
  • von Heusinger , A and Kanzow , C . 2009 . Optimization reformulations of the generalized nash equilibrium problem using Nikaido–Isoda type functions . Comput. Optim. Appl. , 43 : 353 – 377 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.