Barrier Methods for Optimal Control Problems with Convex Nonlinear Gradient Constraints

Please always quote using this URN: urn:nbn:de:0297-zib-11014
  • In this paper we are concerned with the application of interior point methods in function space to gradient constrained optimal control problems, governed by partial differential equations. We will derive existence of solutions together with first order optimality conditions. Afterwards we show continuity of the central path, together with convergence rates depending on the interior point parameter.

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Author:Anton Schiela, Winnifried Wollner
Document Type:ZIB-Report
Tag:convergence of the central path; gradient constrained optimization; interior point method; necessary optimality conditions
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] / 49M05 Methods based on necessary conditions
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C51 Interior-point methods
Date of first Publication:2008/12/10
Series (Serial Number):ZIB-Report (08-47)