## Linear convergence of an interior point method for linear control constrained optimal control problems

Please always quote using this URN: urn:nbn:de:0297-zib-6809

- The paper provides a detailed analysis of a short step interior point algorithm applied to linear control constrained optimal control problems. Using an affine invariant local norm and an inexact Newton corrector, the well-known convergence results from finite dimensional linear programming can be extended to the infinite dimensional setting of optimal control. The present work complements a recent paper of Weiser and Deuflhard, where convergence rates have not been derived. The choice of free parameters, i.e. the corrector accuracy and the number of corrector steps, is discussed.

Author: | Martin Weiser |
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Document Type: | ZIB-Report |

Tag: | inexact Newton methods; infinite dimensional ; interior point methods ; linear optimal control |

MSC-Classification: | 49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Nxx Miscellaneous topics / 49N05 Linear optimal control problems [See also 93C05] |

65-XX NUMERICAL ANALYSIS / 65Jxx Numerical analysis in abstract spaces / 65J10 Equations with linear operators (do not use 65Fxx) | |

65-XX NUMERICAL ANALYSIS / 65Kxx Mathematical programming, optimization and variational techniques / 65K05 Mathematical programming methods [See also 90Cxx] | |

90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C51 Interior-point methods | |

Date of first Publication: | 2002/03/15 |

Series (Serial Number): | ZIB-Report (02-13) |