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.

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Author:Martin WeiserORCiD
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)