Polynomial interior point algorithms for general linear complementarity problems

Tibor Illes, Marianna Nagy, Tamás Terlaky

Research output: Contribution to journalArticlepeer-review


Linear Complementarity Problems (LCPs) belong to the class of NP-complete problems. Therefore we can not expect a polynomial time solution method for LCPs without requiring some special property of the coefficient matrix. Following our recently published ideas we generalize affine scaling and predictor-corrector interior point algorithms to solve LCPs with general matrices in EP-sense, namely, our generalized interior point algorithms either solve the problems with rational coefficient matrix in polynomial time or give a polynomial size certificate that our matrix does not belong to the set of P * (~κ) matrices, with arbitrary large, but apriori fixed, rational, positive ~κ.
Original languageEnglish
Pages (from-to)1-12
Number of pages12
JournalAlgorithmic Operations Research
Issue number1
Publication statusPublished - 1 Jan 2010


  • linear complementarity problem
  • sufficient matrix
  • interior point method
  • affine scaling method
  • predictor-corrector algorithm


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