Optimal Control of Elastic Vector-Valued Allen--Cahn Variational Inequalities
نویسندگان
چکیده
منابع مشابه
Optimal Control of Elastic Vector-Valued Allen-Cahn Variational Inequalities
In this paper we consider a elastic vector-valued Allen-Cahn MPCC (Mathematical Programs with Complementarity Constraints) problem. We use a regularization approach to get the optimality system for the subproblems. By passing to the limit in the optimality conditions for the regularized subproblems, we derive certain generalized first-order necessary optimality conditions for the original problem.
متن کاملA penalty approach to optimal control of Allen-Cahn variational inequalities: MPEC-view
A scalar Allen-Cahn-MPEC problem is considered and a penalization technique is applied to show the existence of an optimal control. We show that the stationary points of the penalized problems converge to weak stationary points of the limit problem.
متن کاملPreconditioning for Allen-Cahn variational inequalities with non-local constraints
The solution of Allen-Cahn variational inequalities with mass constraints is of interest in many applications. This problem can be solved both in its scalar and vector-valued form as a PDE-constrained optimization problem by means of a primal-dual active set method. At the heart of this method lies the solution of linear systems in saddle point form. In this paper we propose the use of Krylov-s...
متن کاملPrimal-dual active set methods for Allen-Cahn variational inequalities
This thesis aims to introduce and analyse a primal-dual active set strategy for solving Allen-Cahn variational inequalities. We consider the standard Allen-Cahn equation with non-local constraints and a vector-valued Allen-Cahn equation with and without non-local constraints. Existence and uniqueness results are derived in a formulation involving Lagrange multipliers for local and non-local con...
متن کاملOptimal control of Allen-Cahn systems
Optimization problems governed by Allen-Cahn systems including elastic effects are formulated and first-order necessary optimality conditions are presented. Smooth as well as obstacle potentials are considered, where the latter leads to an MPEC. Numerically, for smooth potential the problem is solved efficiently by the Trust-Region-NewtonSteihaug-cg method. In case of an obstacle potential firs...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Control and Optimization
سال: 2016
ISSN: 0363-0129,1095-7138
DOI: 10.1137/130937354