Free Access
Volume 47, Number 3, May-June 2013
Page(s) 771 - 787
Published online 04 March 2013
  1. V. Barbu, Optimal control of variational inequalities, Monographs and Studies in Mathematics. Pitman (Advanced Publishing Program), London 24 (1984). [Google Scholar]
  2. M. Bergounioux and F. Mignot, Optimal control of obstacle problems: existence of Lagrange multipliers. ESAIM: COCV 5 (2000) 45–70. [CrossRef] [EDP Sciences] [Google Scholar]
  3. J.F. Bonnans and A. Shapiro, Perturbation analysis of optimization problems. Springer, New York (2000). [Google Scholar]
  4. H. Brezis and G. Stampacchia, Sur la régularité de la solution d’inéquations elliptiques. Bull. Soc. Math. France 96 (1968) 153–180. [Google Scholar]
  5. E. Casas, F. Tröltzsch and A. Unger, Second-order sufficient optimality conditions for a nonlinear elliptic control problem. J. Anal. Appl. 15 (1996) 687–707. [Google Scholar]
  6. A.L. Dontchev, Implicit function theorems for generalized equations. Math. Program. A 70 (1995) 91–106. [Google Scholar]
  7. A. Friedman, Variational principles and free-boundary problems. Pure and Applied Mathematics. John Wiley & Sons Inc., New York (1982). [Google Scholar]
  8. M. Hintermüller and I. Kopacka, Mathematical programs with complementarity constraints in function space: C- and strong stationarity and a path-following algorithm. SIAM J. Optim. 20 (2009) 868–902. [CrossRef] [MathSciNet] [Google Scholar]
  9. M. Hintermüller and I. Kopacka, A smooth penalty approach and a nonlinear multigrid algorithm for elliptic MPECs. Comput. Optim. Appl. 50 (2011) 111–145. [CrossRef] [Google Scholar]
  10. M. Hintermüller, B.S. Mordukhovich and T. Surowiec, Several approaches for the derivation of stationarity conditions for elliptic MPECs with upper-level control constraints. IFB-Report No. 46 (07/2011), Institute of Mathematics and Scientific Computing, University of Graz. [Google Scholar]
  11. M. Hintermüller and T. Surowiec, First-order optimality conditions for elliptic mathematical programs with equilibrium constraints via variational analysis. SIAM J. Optim. 21 (2011) 1561–1593. [CrossRef] [Google Scholar]
  12. L. Hörmander, The Analysis of Partial Differential Operators. Springer (1983). [Google Scholar]
  13. K. Ito and K. Kunisch, Optimal control of elliptic variational inequalities. Appl. Math. Optim. 41 (2000) 343–364. [CrossRef] [MathSciNet] [Google Scholar]
  14. K. Ito and K. Kunisch, On the Lagrange multiplier approach to variational problems and applications, Monographs and Studies in Mathematics. SIAM, Philadelphia 24 (2008). [Google Scholar]
  15. D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and Their Applications. Academic Press, New York (1980). [Google Scholar]
  16. K. Kunisch and D. Wachsmuth, Path-following for optimal control of stationary variational inequalities. Comp. Opt. Appl. 51 (2011) 1345–1373. [CrossRef] [Google Scholar]
  17. K. Kunisch and D. Wachsmuth, Sufficient optimality conditions and semi-smooth Newton methods for optimal control of stationary variational inequalities. ESAIM: COCV 18 (2012). [CrossRef] [EDP Sciences] [Google Scholar]
  18. F. Mignot, Contrôle dans les inéquations variationelles elliptiques. J. Funct. Anal. 22 (1976) 130–185. [CrossRef] [Google Scholar]
  19. F. Mignot and J.-P. Puel, Optimal control in some variational inequalities. SIAM J. Control Optim. 22 (1984) 466–476. [CrossRef] [MathSciNet] [Google Scholar]
  20. J. Outrata, J. Jarušek and J. Stará, On optimality conditions in control of elliptic variational inequalities. Set-Valued Var. Anal. 19 (2011) 23–42. [CrossRef] [MathSciNet] [Google Scholar]
  21. H. Scheel and S. Scholtes, Mathematical programs with complementarity constraints: stationarity, optimality, and sensitivity. Math. Oper. Res. 25 (2000) 1–22. [CrossRef] [MathSciNet] [Google Scholar]
  22. G. Stampacchia, Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus. Ann. Inst. Fourier (Grenoble) 15 (1965) 189–258. [CrossRef] [MathSciNet] [Google Scholar]
  23. G. Wachsmuth, Private communication (2012). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you