Mathematical Programming

, Volume 86, Issue 2, pp 261–282 | Cite as

Basis- and partition identification for quadratic programming and linear complementarity problems

  • Arjan B. Berkelaar
  • Benjamin Jansen
  • Kees Roos
  • Tamás Terlaky

Abstract.

Optimal solutions of interior point algorithms for linear and quadratic programming and linear complementarity problems provide maximally complementary solutions. Maximally complementary solutions can be characterized by optimal partitions. On the other hand, the solutions provided by simplex–based pivot algorithms are given in terms of complementary bases. A basis identification algorithm is an algorithm which generates a complementary basis, starting from any complementary solution. A partition identification algorithm is an algorithm which generates a maximally complementary solution (and its corresponding partition), starting from any complementary solution. In linear programming such algorithms were respectively proposed by Megiddo in 1991 and Balinski and Tucker in 1969. In this paper we will present identification algorithms for quadratic programming and linear complementarity problems with sufficient matrices. The presented algorithms are based on the principal pivot transform and the orthogonality property of basis tableaus.

Key words: basis recovery – partition – principal pivot transforms – Balinski-Tucker tableaus – quadratic programming – linear complementarity problems – interior point methods – sufficient matrices – crossover – Criss-Cross method 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Arjan B. Berkelaar
    • 1
  • Benjamin Jansen
    • 2
  • Kees Roos
    • 3
  • Tamás Terlaky
    • 3
  1. 1.Econometric Institute, Faculty of Economics, Erasmus University Rotterdam, The NetherlandsNL
  2. 2.Centre for Quantitative Methods (CQM) B.V., Eindhoven, The NetherlandsNL
  3. 3.Department of Statistics, Probability and Operations Research, Faculty of Technical Mathematics and Computer Science, Delft University of Technology, The NetherlandsNL

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