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) |
| ZIB-Reportnumber: | 04-47 |
| Published in: | Appeared in: Computational Optimization and Applications 39, No. 2 (2008) 183-218 |
