Superlinear Convergence of the Control Reduced Interior Point Method for PDE Constrained Optimization

Please always quote using this URN: urn:nbn:de:0297-zib-8490
  • A thorough convergence analysis of the Control Reduced Interior Point Method in function space is performed. This recently proposed method is a primal interior point pathfollowing scheme with the special feature, that the control variable is eliminated from the optimality system. Apart from global linear convergence we show, that this method converges locally almost quadratically, if the optimal solution satisfies a function space analogue to a non-degeneracy condition. In numerical experiments we observe, that a prototype implementation of our method behaves in compliance with our theoretical results.

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Metadaten
Author:Anton Schiela, Martin WeiserORCiD
Document Type:ZIB-Report
Tag:interior point methods in function space; optimal control; superlinear convergence
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
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C51 Interior-point methods
Date of first Publication:2005/02/09
Series (Serial Number):ZIB-Report (05-15)
Published in:Appeared in: Comp. Opt. and Appl. 39(3): 369-393, 2008