POD based inexact SQP methods for optimal control problems governed by a semilinear heat equation

Abstract

This diploma thesis is focused on the application of a POD based inexact SQP method to an optimal control problem governed by a semilinear heat equation. The theoretical foundation for the solution theory of the optimal control problem is laid by discussing the unique solvability of the state equation, investigating the existence of an optimal solution and deriving necessary optimality conditions utilizing the Lagrange technique. Due to the nonlinearity, the discussion of second order sufficient optimality criteria is needed. The numerical solution of the optimal control problem is realized by an inexact SQP method. To illustrate the presented SQP strategy, numerical test examples are carried out and discussed in detail. A POD based model reduction is applied and persues the aim to decrease computational complexity of the high-dimensional FE systems while providing solutions of good accuracy.