Publication Cover
Applicable Analysis
An International Journal
Volume 88, 2009 - Issue 8
373
Views
7
CrossRef citations to date
0
Altmetric
Original Articles

Robust optimization with applications to game theory

, &
Pages 1183-1195 | Received 06 Dec 2008, Accepted 12 Jun 2009, Published online: 21 Sep 2010

References

  • Nash , J . 1950 . Equilibrium points in N-person games . Proc. Nat. Acad. Sci. USA , 36 : 48 – 49 .
  • Nash , J . 1951 . Non-cooperative games . Ann of Math. , 54 : 286 – 295 .
  • Harsanyi , J . 1967, 1968 . Games with incomplete information played by ‘Bayesian’ players, I–III . Manag. Sci. , 14 : 159 – 182 . 320–334, 486–502
  • Pang , JS and Fukushima , M . 2005 . Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games . Comput. Manag. Sci. , 2 : 21 – 56 .
  • Facchinei , F , Fischer , A and Piccialli , V . 2007 . On generalized Nash games and variational inequalities . Oper. Res. Lett. , 35 : 159 – 164 .
  • Facchinei , F , Fischer , A and Piccialli , V . 2009 . Generalized Nash equilibrium problems and Newton methods . Math. Program. , 117 : 163 – 194 .
  • Aghassi , M and Bertsimas , D . 2006 . Robust game theory . Math. Prog. , 107 : 231 – 273 .
  • Ben-Tal , A and Nemirovski , A . 1999 . Robust solutions of uncertain linear programs . Oper. Res. Lett. , 25 : 1 – 13 .
  • Ben-Tal , A and Nemirovski , A . 2000 . Robust solutions of linear programming problems contaminated with uncertain data . Math. Program. , 88 : 411 – 421 .
  • Ben-Tal , A and Nemirovski , A . 2007 . Selected topics in robust convex optimization . Math. Program. , 112 : 125 – 158 .
  • Bertsimas , D , Pachamanova , D and Sim , M . 2004 . Robust linear optimization under general norms . Oper. Res. Lett. , 32 : 510 – 516 .
  • Facchinei , F and Pang , JS . 2003 . Finite-dimensional Variational Inequalities and Complementarity Problems , Vol. I and II , New York : Springer-Verlag .
  • Chen , XD , Sun , D and Sun , J . 2003 . Complementarity functions and numerical experiments on some smoothing Newton methods for second-order-cone complementarity problem . Comput. Optim. Appl. , 25 : 39 – 56 .
  • Fukushima , M , Luo , Z-Q and Tseng , P . 2001 . Smoothing functions for second-order cone complementarity problems . SIAM J. Optim. , 12 : 436 – 460 .
  • Freund , RM and Ordóñez , F . 2005 . On an extension of conditional number theory to nonconic convex optimization . Math. Oper. Res. , 30 : 173 – 194 .
  • Lobo , MS , Vandenberghe , L , Boyd , S and Lebret , H . 1998 . Applications of second-order cone programming . Linear Algebra Appl. , 284 : 193 – 228 .
  • Bertsimas , D and Sim , M . 2006 . Tractable approximations to robust conic optimization problems . Math. Program. , 107 : 5 – 36 .
  • Hayashi , S , Yamashita , N and Fukushima , M . 2005 . Robust Nash equilibria and second-order cone complementarity problems . J. Nonlinear Convex Anal. , 6 : 283 – 296 .
  • Hayashi , S , Yamashita , N and Fukushima , M . 2005 . A combined smoothing and regularization method for monotone second-order cone complementarity problems . SIAM J. Optim. , 15 : 593 – 615 .

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.