Numerical solution of control-state constrained optimal control problems with an inexact smoothing Newton method

• Published in: IMA journal of numerical analysis Vol. 31; no. 4; pp. 1598 - 1624
• Main Authors: Chen, Jinhai, Gerdts, Matthias
• Format: Journal Article
• Language: English
• Published: Oxford Oxford University Press 01.10.2011
• Subjects: Calculus of variations and optimal control; Convergence; Exact sciences and technology; Global analysis, analysis on manifolds; Mathematical analysis; Mathematical models; Mathematics; Newton methods; Norms; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Optimal control; Sciences and techniques of general use; Smoothing; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; optimal control; control-state constraints; inexact smoothing Newton method; global convergence; Smoothing methods; Numerical method; Convergence; Necessary condition; Numerical analysis; Numerical solution; Optimal control; Optimal solution; Smooth function; Mixed problem; Newton method; State constraint
• ISSN: 0272-4979; 1464-3642
• DOI: 10.1093/imanum/drq023

This paper analyses a globalized inexact smoothing Newton method for the numerical solution of optimal control problems subject to mixed control-state constraints. The method uses the smoothed Fischer-Burmeister function to reformulate first-order necessary conditions and aims at minimizing the squared residual norm using Newton steps and gradient-like steps. Numerical experiments are provided to illustrate the convergence results.