Numerical Solution of Optimal Control Problems with Sparse SQP-Methods

Georg Wimmer (), Thorsten Steinmetz () and Markus Clemens ()
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Georg Wimmer: University of the Federal Armed Forces Hamburg, Chair for Theory of Electrical Engineering and Computational Electromagnetics Helmut-Schmidt-University
Thorsten Steinmetz: University of the Federal Armed Forces Hamburg, Chair for Theory of Electrical Engineering and Computational Electromagnetics Helmut-Schmidt-University
Markus Clemens: University of the Federal Armed Forces Hamburg, Chair for Theory of Electrical Engineering and Computational Electromagnetics Helmut-Schmidt-University

A chapter in Numerical Mathematics and Advanced Applications, 2006, pp 996-1003 from Springer

Abstract: Abstract Many physical processes can be modelled mathematically by ordinary differential equations. If such a process is governed by control variables an optimal control problem can be formulated. The basic problem is to choose the control variables such that some objective function is optimized while satisfying the differential equations. Approximating the control variables by linear functions and the state variables by low order Runge-Kutta schemes results in a nonlinear sparse constrained optimization problem. The inner iteration of a SQP-algorithm consists in solving an equality constrained quadratic optimization problem with a positive definite system matrix and a sparse constraint matrix. This optimization problem can be solved effectively by a projected cg-method when using a sparse LU decomposition of the constraint matrix.

Keywords: Optimal Control Problem; Merit Function; Adjoint Variable; Matrix Vector Product; Quadratic Optimization Problem (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1007/978-3-540-34288-5_99

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