Free Access
Issue |
ESAIM: COCV
Volume 21, Number 1, January-March 2015
|
|
---|---|---|
Page(s) | 271 - 300 | |
DOI | https://doi.org/10.1051/cocv/2014024 | |
Published online | 09 December 2014 |
- V. Barbu, Optimal Control of Variational Inequalities, vol. 100 of Res. Notes Math. Pitman, Boston (1984). [Google Scholar]
- M. Bergounioux, Optimal control problems governed by abstract elliptic variational inequalities with state constraints. SIAM J. Control Optim. 36 (1998) 273–289. [CrossRef] [MathSciNet] [Google Scholar]
- F. Bonnans and D. Tiba, Pontryagin’s principle in the control of semilinear elliptic variational inequalities. Appl. Math. Optim. 23 (1991) 299–312. [CrossRef] [MathSciNet] [Google Scholar]
- E. Casas, J.C. de los Reyes, and F. Tröltzsch, Sufficient second-order optimality conditions for semilinear control problems with pointwise state constraints. SIAM J. Optim. 19 (2008) 616–643. [CrossRef] [MathSciNet] [Google Scholar]
- E. Casas and M. Mateos, Second order optimality conditions for semilinear elliptic control problems with finitely many state constraints. SIAM J. Control Optim. 40 (2002) 1431–1454. [CrossRef] [MathSciNet] [Google Scholar]
- E. Casas and F. Tröltzsch, First- and second order optimality conditions for a class of optimal control problems with quasilinear ellitpic equations. SIAM J. Control Optim. 48 (2009) 688–718. [CrossRef] [MathSciNet] [Google Scholar]
- E. Casas, F. Tröltzsch, and A. Unger, Second order sufficient optimality conditions for a nonlinear elliptic control problem. Zeitschrift für Analysis und ihre Anwendungen 15 (1996) 687–707. [CrossRef] [MathSciNet] [Google Scholar]
- K. Gröger, A W1,p-estimate for solutions to mixed boundary value problems for second order elliptic differential equations. Mathematische Annalen 283 (1989) 679–687. [Google Scholar]
- P. Grisvard, Elliptic Problems in Nonsmooth Domains. Pitman, Boston (1985). [Google Scholar]
- R. Haller-Dintelmann, C. Meyer, J. Rehberg, and A. Schiela, Hölder continuity and optimal control for nonsmooth elliptic problems. Appl. Math. Optim. 60 (2009) 397–428. [CrossRef] [MathSciNet] [Google Scholar]
- W. Han and B.D. Reddy, Plasticity. Springer, New York (1999). [Google Scholar]
- R. Herzog and C. Meyer, Optimal control of static plasticity with linear kinematic hardening. J. Appl. Math. Mech. 91 (2011) 777–794. [Google Scholar]
- R. Herzog, C. Meyer, and G. Wachsmuth, Integrability of displacement and stresses in linear and nonlinear elasticity with mixed boundary conditions. J. Math. Anal. Appl. 382 (2011) 802–813. [CrossRef] [Google Scholar]
- R. Herzog, C. Meyer, and G. Wachsmuth, C-stationarity for optimal control of static plasticity with linear kinematic hardening. SIAM J. Control Optim. 50 (2012) 3052–3082. [CrossRef] [MathSciNet] [Google Scholar]
- R. Herzog, C. Meyer, and G. Wachsmuth, B- and strong stationarity for optimal control of static plasticity with hardening. SIAM J. Optim. 23 (2013) 321–352. [CrossRef] [Google Scholar]
- 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]
- M. Hintermüller and Th. Surowiec, First order optimality conditions for elliptic mathematical programs with equilibrium constraints via variational analysis. SIAM J. Optim. 21 (2012) 1561–1593. [CrossRef] [Google Scholar]
- K. Ito and K. Kunisch, Optimal control of elliptic variational inequalities. Appl. Math. Optim. 41 (2000) 343–364. [CrossRef] [MathSciNet] [Google Scholar]
- C. Kanzow and A. Schwartz, Mathematical programs with equilibrium constraints: enhanced Fritz John-conditions, new constraint qualifications, and improved exact penalty results. SIAM J. Optim. 20 (2010) 2730–2753. [CrossRef] [Google Scholar]
- K. Kunisch and D. Wachsmuth, Sufficient optimality conditions and semi-smooth newton methods for optimal control of stationary variational inequalities. ESAIM: COCV 18 (2012) 520–547. [CrossRef] [EDP Sciences] [Google Scholar]
- K. Kunisch and D. Wachsmuth, Path-following for optimal control of stationary variational inequalities. Comput. Optim. Appl. (2012) 1–29. [Google Scholar]
- F. Mignot, Contrôle dans les inéquations variationelles elliptiques. J. Funct. Anal. 22 (1976) 130–185. [CrossRef] [Google Scholar]
- F. Mignot and J.-P. Puel, Optimal control in some variational inequalities. SIAM J. Control Optim. 22 (1984) 466–476. [CrossRef] [MathSciNet] [Google Scholar]
- P. Neff and D. Knees, Regularity up to the boundary for nonlinear elliptic systems arising in time-incremental infinitesimal elasto-plasticity. SIAM J. Math. Anal. 40 (2008) 21–43. [CrossRef] [MathSciNet] [Google Scholar]
- 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]
- 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]
- G. Wachsmuth, Optimal control of quasistatic plasticity – An MPCC in function space. Ph.D. thesis, Chemnitz University of Technology, Germany (2011). [Google Scholar]
- G. Wachsmuth, Differentiability of implicit functions: Beyond the implicit function theorem. Technical Report SPP1253-137, Priority Program 1253, German Research Foundation (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.