Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/a-relaxation-approach-to-vector-valued-allen-cahn-mpec-problems-myqg9YeO26
References (29)
-
L Blank, H Garcke, L Sarbu, V Styles (2013)
Primal-dual active set methods for Allen–Cahn variational inequalities with non-local constraintsNumer. Methods PDEs, 29
-
F. Mignot, J. Puel (1984)
Optimal control in some variational inequalitiesBanach Center Publications, 14
-
M. Farshbaf-Shaker (2012)
A Penalty Approach to Optimal Control of Allen-Cahn Variational Inequalities: MPEC-ViewNumerical Functional Analysis and Optimization, 33
-
ZQ Luo, JS Pang, D Ralph (1996)
Mathematical Programs with Equilibrium Constraints -
Karl KunischyOctober (2007)
Optimal Control of Elliptic Variational Inequalities -
F Mignot, JP Puel (1984)
Optimal control in some variational inequalitiesSIAM J. Control Optim., 22
-
M. Bergounioux, S. Lenhart (2004)
Optimal Control of Bilateral Obstacle ProblemsSIAM J. Control. Optim., 43
-
M. Hintermüller, Moulay Tber (2010)
An Inverse Problem in American Options as a Mathematical Program with Equilibrium Constraints: C-Stationarity and an Active-Set-Newton SolverSIAM J. Control. Optim., 48
-
H. Garcke (2005)
On a Cahn-Hilliard model for phase separation with elastic misfitAnnales De L Institut Henri Poincare-analyse Non Lineaire, 22
-
R. Herzog, C. Meyer (2011)
Optimal control of static plasticity with linear kinematic hardeningZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 91
-
F. Patrone (1975)
On the Optimal Control of Variational Inequalities -
(2007)
Control of Free Boundaries -
(1985)
Optimal Control of Variational Inequalities: Optimality Conditions and Numerical Methods, Free Boundary Problems: Applications and Theory, Vol IV, Bossavit -
G. M.
Partial Differential EquationsNature, 75
-
J. Zowe, S. Kurcyusz (1979)
Regularity and stability for the mathematical programming problem in Banach spacesApplied Mathematics and Optimization, 5
-
L. Blank, H. Garcke, L. Sarbu, V. Styles (2013)
Nonlocal Allen–Cahn systems: analysis and a primal–dual active set methodIma Journal of Numerical Analysis, 33
-
A Friedman (1986)
Optimal control for variational inequalitiesSIAM J. Control Optim., 24
-
L. Blank, H. Garcke, L. Sarbu, V. Styles (2010)
Primal‐dual active set methods for Allen–Cahn variational inequalities with nonlocal constraintsNumerical Methods for Partial Differential Equations, 29
-
(1993)
Analysis and Control of Non Linear Infinite Dimensional Systems -
M. Brokate, J. Sprekels (1996)
Hysteresis and Phase Transitions -
H. Garcke (2007)
ON MATHEMATICAL MODELS FOR PHASE SEPARATION IN ELASTICALLY STRESSED SOLIDS -
(1996)
Applied Mathematical Sciences 121 -
M. Bergounioux (1997)
Optimal control of an obstacle problemApplied Mathematics and Optimization, 36
-
M. Bergounioux, H. Zidani (1999)
Pontryagin Maximum Principle for Optimal Control of Variational InequalitiesSiam Journal on Control and Optimization, 37
-
A. Friedman (1987)
Optimal control for parabolic variational inequalitiesSiam Journal on Control and Optimization, 25
-
J. Bonnans, D. Tiba (1991)
Pontryagin's principle in the control of semilinear elliptic variational inequalitiesApplied Mathematics and Optimization, 23
-
M. Hintermüller, I. Kopacka (2009)
Mathematical Programs with Complementarity Constraints in Function Space: C- and Strong Stationarity and a Path-Following AlgorithmSIAM J. Optim., 20
-
K Ito, K Kunisch (2010)
Optimal control of parabolic variational inequalitiesJ. Math. Pures Appl., 93
-
Zheng-Xu He (1987)
State constrained control problems governed by variational inequalitiesSiam Journal on Control and Optimization, 25
- Publisher
- Springer Journals
- Copyright
- Copyright © 2015 by Springer Science+Business Media New York
- Subject
- Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics
- ISSN
- 0095-4616
- eISSN
- 1432-0606
- DOI
- 10.1007/s00245-014-9282-0
- Publisher site
- See Article on Publisher Site
Abstract
In this paper we consider a vector-valued Allen–Cahn MPEC problem. To derive optimality conditions we exploit a regularization–relaxation technique. The optimality system of the regularized–relaxed subproblems are investigated by applying the classical result of Zowe and Kurcyusz. Finally we show that the stationary points of the regularized–relaxed subproblems converge to weak stationary points of the limit problem.
Journal
Applied Mathematics and Optimization – Springer Journals
Published: Oct 1, 2015