The Central Path towards the Numerical Solution of Optimal Control Problems

Please always quote using this URN: urn:nbn:de:0297-zib-6380
  • A new approach to the numerical solution of optimal control problems including control and state constraints is presented. Like hybrid methods, the approach aims at combining the advantages of direct and indirect methods. Unlike hybrid methods, however, our method is directly based on interior-point concepts in function space --- realized via an adaptive multilevel scheme applied to the complementarity formulation and numerical continuation along the central path. Existence of the central path and its continuation towards the solution point is analyzed in some theoretical detail. An adaptive stepsize control with respect to the duality gap parameter is worked out in the framework of affine invariant inexact Newton methods. Finally, the performance of a first version of our new type of algorithm is documented by the successful treatment of the well-known intricate windshear problem.

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Author:Martin WeiserORCiD, Peter Deuflhard
Document Type:ZIB-Report
Tag:affine invariance; interior point methods; optimal control
MSC-Classification:49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Mxx Numerical methods [See also 90Cxx, 65Kxx] / 49M15 Newton-type methods
65-XX NUMERICAL ANALYSIS / 65Kxx Mathematical programming, optimization and variational techniques / 65K10 Optimization and variational techniques [See also 49Mxx, 93B40]
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C48 Programming in abstract spaces
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C51 Interior-point methods
Date of first Publication:2001/06/07
Series (Serial Number):ZIB-Report (01-12)
Published in:Appeared under the title " Inexact Central Path Following Algorithms for Optimal Control Problems" in: SIAM J. Contr. Opt. 46 (3) (2007) 792-815