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.

Download full text files

Export metadata

Additional Services

Share in Twitter Search Google Scholar
Metadaten
Author:Uwe Prüfert, Fredi Tröltzsch, Martin Weiser
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