Optimal Control for an Elliptic System with Pointwise Nonlinear Control Constraints
نویسندگان
چکیده
Optimal control for an elliptic system with pointwise Euclidean norm constraints on the control variables is investigated. First order optimality conditions are derived in a manner that is amenable for numerical realisation. An efficient semi-smooth Newton algorithm is proposed based on this optimality system. Numerical examples are given to validate the superlinear convergence of the semismooth Newton algorithm.
منابع مشابه
Existence of Regular Lagrange Multipliers for a Nonlinear Elliptic Optimal Control Problem with Pointwise Control-State Constraints
A class of optimal control problems for semilinear elliptic equations with mixed control-state constraints is considered. The existence of bounded and measurable Lagrange multipliers is proven. As a particular application, the Lavrentiev type regularization of pointwise state constraints is discussed. Here, the existence of associated regular multipliers is shown, too.
متن کاملSecond Order Sufficient Optimality Conditions for Some State-constrained Control Problems of Semilinear Elliptic Equations
This paper deals with a class of optimal control problems governed by elliptic equations with nonlinear boundary condition. The case of boundary control is studied. Pointwise constraints on the control and certain equality and set{constraints on the state are considered. Second order suucient conditions for local optimality of controls are established.
متن کاملOn Finite Element Error Estimates for Optimal Control Problems with Elliptic PDEs
Discretizations of optimal control problems for elliptic equations by finite element methods are considered. The problems are subject to constraints on the control and may also contain pointwise state constraints. Some techniques are surveyed to estimate the distance between the exact optimal control and the associated optimal control of the discretized problem. As a particular example, an erro...
متن کاملSecond Order Su cient Optimality Condition for a Nonlinear Elliptic Boundary Control Problem
In this paper suucient second order optimality conditions are established for optimal control problems governed by a linear elliptic equation with nonlinear boundary condition, where pointwise constraints on the control are given. The second order condition requires the coercivity of the Lagrange{function on a suitable subspace together with rst order suucient conditions on a certain set of str...
متن کاملOn Regularity of Solutions and Lagrange Multipliers of Optimal Control Problems for Semilinear Equations with Mixed Pointwise Control-State Constraints
A class of nonlinear elliptic and parabolic optimal control problems with mixed control-state constraints is considered. Extending a method known for the control of ordinary differential equations to the case of PDEs, the Yosida-Hewitt theorem is applied to show that the Lagrange multipliers are functions of certain Lp-spaces. By bootstrapping arguments, under natural assumptions, optimal contr...
متن کامل