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A Control Reduced Primal Interior Point Method for PDE Constrained Optimization

Please always quote using this URN: urn:nbn:de:0297-zib-8138
  • A primal interior point method for control constrained optimal control problems with PDE constraints is considered. Pointwise elimination of the control leads to a homotopy in the remaining state and dual variables, which is addressed by a short step pathfollowing method. The algorithm is applied to the continuous, infinite dimensional problem, where discretization is performed only in the innermost loop when solving linear equations. The a priori elimination of the least regular control permits to obtain the required accuracy with comparable coarse meshes. Convergence of the method and discretization errors are studied, and the method is illustrated at two numerical examples.

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Author:Martin WeiserORCiD, Tobias Gänzler, Anton Schiela
Document Type:ZIB-Report
Tag:discretization error; finite elements; interior point methods in function space; 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 / 65Nxx Partial differential equations, boundary value problems / 65N15 Error bounds
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C51 Interior-point methods
Date of first Publication:2004/09/07
Series (Serial Number):ZIB-Report (04-38)
Published in:Appeared under the title "Control Reduced Primal Interior Point Methods" in: Comp. Optim. and Appl. 41 (2008) pp. 127-145
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