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The convergence of an interior point method for an elliptic control problem with mixed control-state constraints

Please always quote using this URN: urn:nbn:de:0297-zib-8223
  • The paper addresses primal interior point method for state constrained PDE optimal control problems. By a Lavrentiev regularization, the state constraint is transformed to a mixed control-state constraint with bounded Lagrange multiplier. Existence and convergence of the central path are established, and linear convergence of a short-step pathfollowing method is shown. The behaviour of the regularizations are demonstrated by numerical examples.

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Author:Uwe Prüfert, Fredi Tröltzsch, Martin WeiserORCiD
Document Type:ZIB-Report
Tag:Lavrentiev regularization; interior point methods in function space; mixed control-state constraints; optimal control
MSC-Classification:49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Jxx Existence theories / 49J20 Optimal control problems involving partial differential equations
65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M15 Error bounds
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C51 Interior-point methods
Date of first Publication:2004/12/01
Series (Serial Number):ZIB-Report (04-47)
Published in:Appeared in: Computational Optimization and Applications 39, No. 2 (2008) 183-218