Optimal Control for the Elliptic System with Polygonal State Constraints
نویسنده
چکیده
This work is devoted to stationary optimal control problems with polygonal constraints on the components of the state. Existence of Lagrange multipliers, of different regularity, is verified for the cases with and without Slater condition holding. For the numerical realization a semi-smooth Newton method is proposed for an appropriately chosen family of regularized problems. The asymptotic behavior of the regularized problem class is studied, and numerical feasibility of the method is shown.
منابع مشابه
Optimal Control on an Elliptic System with Convex Polygonal Control Constraints
The semi-smooth Newton method for optimal control problems for systems of partial differential equations with polygonal constraints on the controls is developed. The Newton derivatives are characterized for the case of systems of dimension two, superlinear convergence is verified, and a simple proof-of-concept numerical example is provided.
متن کاملOptimal Control for an Elliptic System with Polygonal State Constraints
This work is devoted to stationary optimal control problems with polygonal constraints on the components of the state. Existence of Lagrange multipliers, of different regularity, is verified for the cases with and without Slater condition holding. For the numerical realization a semi-smooth Newton method is proposed for an appropriately chosen family of regularized problems. The asymptotic beha...
متن کاملOptimal Control of Elliptic Equations with Pointwise Constraints on the Gradient of the State in Nonsmooth Polygonal Domains
This article is concerned with optimal control problems subject to a second order elliptic PDE and additional pointwise constraints on the gradient of the state. In particular, existence of solutions on nonsmooth polygonal or polyhedral domains is analyzed. In this situation the solution operator for the partial differential equation does not provide enough regularity to state the pointwise con...
متن کاملError Estimates for the Numerical Approximation of Dirichlet Boundary Control for Semilinear Elliptic Equations
We study the numerical approximation of boundary optimal control problems governed by semilinear elliptic partial differential equations with pointwise constraints on the control. The control is the trace of the state on the boundary of the domain, which is assumed to be a convex, polygonal, open set in R. Piecewise linear finite elements are used to approximate the control as well as the state...
متن کاملOptimal Control in Nonconvex Domains: a Priori Discretization Error Estimates
An optimal control problem for a 2-d elliptic equation is investigated with pointwise control constraints. The domain is assumed to be polygonal but non-convex. The corner singularities are treated by a priori mesh grading. Approximations of the optimal solution of the continuous optimal control problem will be constructed by a projection of the discrete adjoint state. It is proved that these a...
متن کامل