Rigorous error bounds for the optimal value in semidefinite programming

Link:
Autor/in:
Verlag/Körperschaft:
Hamburg University of Technology
Erscheinungsjahr:
2007
Medientyp:
Text
Schlagworte:
  • Interval arithmetic
  • Linear programming
  • NETLIB LP library
  • Rigorous error bounds
  • SDPLIB
  • Semidefinite programming
  • Sensitivity analysis
  • 004: Informatik
  • 510: Mathematik
Beschreibung:
  • A wide variety of problems in global optimization, combinatorial optimization, as well as systems and control theory can be solved by using linear and semidefinite programming. Sometimes, due to the use of floating point arithmetic in combination with ill-conditioning and degeneracy, erroneous results may be produced. The purpose of this article is to show how rigorous error bounds for the optimal value can be computed by carefully postprocessing the output of a linear or semidefinite programming solver. It turns out that in many cases the computational costs for postprocessing are small compared to the effort required by the solver. Numerical results are presented including problems from the SDPLIB and the NETLIB LP library; these libraries contain many ill-conditioned and real-life problems.
Beziehungen:
DOI 10.1137/050622870
Quellsystem:
TUHH Open Research

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Quelldatensatz
oai:tore.tuhh.de:11420/8659