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Preprint 33-2005

An SQP Active Set Method for a Semilinear Optimal Control Problem with Nonlocal Radiation Interface Conditions

Source file is available as :   Portable Document Format (PDF)

Author(s) : Christian Meyer

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 33-2005

MSC 2000

49M37 Methods of nonlinear programming type
65R20 Integral equations

Abstract :
We consider a sequential quadratic programming (SQP) method for the solution of an optimal control problem governed by a semilinear elliptic equation with nonlocal interface conditions. These conditions arise from conductive-radiative heat transfer in non-convex domains. After stating first- and second-order optimality conditions, we introduce the SQP algorithm that uses an active set method to solve the linear quadratic subproblems arising in each step. The corresponding optimality systems are discretized by linear finite elements, using a partly exact summarized midpoint rule for the discretization of the nonlocal radiation interface conditions. The paper ends with some numerical results demonstrating the efficiency of the proposed method.

Keywords : Optimal control, semilinear elliptic equations, onlocal interface conditions, sequential quadratic programming, active set strategy

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