Publication Cover
Optimization
A Journal of Mathematical Programming and Operations Research
Volume 65, 2016 - Issue 5
212
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

A note on stability of stationary points in mathematical programs with generalized complementarity constraints

Pages 1049-1060 | Received 01 Dec 2014, Accepted 28 Sep 2015, Published online: 07 Nov 2015

References

  • Luo Z-Q, Pang J-S, Ralph D. Mathematical programs with equilibrium constraints. Cambridge: Cambridge University Press; 1996.
  • Outrata JV, Kočvara M, Zowe J. Nonsmooth aproach to optimization problems with equilibrium contraints. Dordrecht: Kluwer Academic Publishers; 1998.
  • Dempe S. Foundations of bi-level programming. Dordrecht: Kluwer Academic Publishers; 2002.
  • Sheel H, Scholtes S. Mathematical programs with complementarity constraints: stationarity, optimality and sensitivity. Math. Oper. Res. 2000;25:1–22.
  • Lucet Y, Ye J. Sensitivity analysis on the value function for optimization problems with variational inequality constraints. SIAM J. Control Optim. 2001;40:699–723. [Erratum: SIAM J. Control Optim. 2001;41:1315–1319.]
  • Hu X, Ralph D. A note on sensitivity of value functions of mathematical programs with complementarity constraints. Math. Prog. 2002;93:265–279.
  • Dempe S, Mordukhovich BS, Zemkoho AB. Sensitivity analysis for two-level value functions with applications to bilevel programming. SIAM J. Optim. 2012;22:1309–1343.
  • Jongen HT, R\"{u}ckmann J-J, Shikhman V. On stability of the feasible set of a mathematical problem with complementarity constraints. SIAM J. Optim. 2009;20:1171–1184.
  • Jongen HT, Shikhman V, Steffensen S. Characterization of strong stability for C-stationary points in MPCC. Math. Prog. 2012;132:295–308.
  • Kojima M. Strongly stable stationary solutions in nonlinear programming. In: Robinson SM, editor. Analysis and computation of fixed points. New York (NY): Academy Press; 1980. p. 93–138.
  • Červinka M, Outrata JV, Pištěk M. On stability of M-stationary points in MPCCs. Set-Valued Var. Anal. 2014;22:575–595.
  • Henrion R, Jourani A, Outrata JV. On the calmness of a class of multifunctions. SIAM J. Optim. 2002;13:603–618.
  • Ioffe AD, Outrata JV. On metric and calmness qualification conditions in subdifferential calculus. Set-Valued Anal. 2008;16:199–227.
  • Fletcher R, Leyffer S. Solving mathematical program with complementarity constraints as nonlinear programs. Optim. Methods Softw. 2004;19:15–40.
  • Kanzow C, Schwartz A. The price of inexactness: convergence properties of relaxation methods for mathematical programs with equilibrium constraints revisited. Math. Oper. Res. 2015;40:253–275.
  • Outrata JV. Optimality conditions for a class of mathematical programs with equilibrium constraints. Math. Oper. Res. 1999;24:627–644.
  • Ye JJ, Ye XY. Necessary optimality conditions for optimization problems with variational inequality constraints. Math. Oper. Res. 1997;22:977–997.
  • Ye JJ. Constraint qualifications and necessary optimality conditions for optimization problems with variational inequality constraints. SIAM J. Optim. 2000;10:943–962.
  • Adam L, Červinka M, Pištěk M. Normally admissible stratification and calculation of normal cones to a finite union of polyhedral sets. Set-Valued Var. Anal. Forthcoming 2015.
  • Rockafellar RT, Wets RJ-B. Variational analysis. Vol. 317, A series of comprehensive studies in mathematics. Berlin: Springer Verlag; 1998.
  • Dontchev AL, Rockafellar RT. Implicit functions and solution mappings. Heidelberg: Springer Verlag; 2009.
  • Mordukhovich BS. Sensitivity analysis in nonsmooth optimization. In: Field DA, Komkov V, editors. Theoretical aspects of industrial design. SIAM Proceedings in Applied Mathematics. Vol. 58. Philadelphia, PA: SIAM Publications; 1992. p. 32–46.

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.