A Simplified Newton Method to Generate Snapshots for POD Models of Semilinear Optimal Control Problems

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

A Method for Solving Optimal Control Problems Using Genetic Programming

This paper deals with a novel method for solving optimal control problems based on genetic programming. This approach produces some trial solutions and seeks the best of them. If the solution cannot be expressed in a closed analytical form then our method produces an approximation with a controlled level of accuracy. Using numerical examples, we will demonstrate how to use the results.

Trust-Region POD using A-Posteriori Error Estimation for Semilinear Parabolic Optimal Control Problems

An optimal control problem governed by a semilinear heat equation is solved using a globalized inexact Newton method. To reduce the computational effort a model order reduction approach based on proper orthogonal decomposition (POD) is applied. Within a trust region framework we guarantee that the reducedorder models are sufficiently accurate by ensuring gradient accuracy. The gradient error is...

A semismooth Newton method for a class of semilinear optimal control problems with box and volume constraints

In this paper we consider optimal control problems subject to a semilinear elliptic state equation together with the control constraints 0 ≤ u ≤ 1 and ∫ u = m. Optimality conditions for this problem are derived and reformulated as a nonlinear, nonsmooth equation which is solved using a semismooth Newton method. A regularization of the nonsmooth equation is necessary to obtain the superlinear co...

Convergence of the Lagrange-newton Method for Optimal Control Problems

Convergence results for two Lagrange-Newton-type methods of solving optimal control problems are presented. It is shown how the methods can be applied to a class of optimal control problems for nonlinear ODEs, subject to mixed control-state constraints. The first method reduces to an SQP algorithm. It does not require any information on the structure of the optimal solution. The other one is th...