Verification for existence of solutions of linear complementarity problems

Xiaojun Chen, Yukihiro Shogenji, Maretsugu Yamasaki

Research output: Journal article publicationJournal articleAcademic researchpeer-review

4 Citations (Scopus)


Recently, G. Alefeld, X. Chen and F. Potra [Numer. Math. 83 (1999) 265-315] presented a verification method for solutions of linear complementarity problems (LCPs). This paper is an attempt to obtain more useful information from the output of this verification method. In particular, existing results can only claim the nonexistence of solutions in a given interval. We will use the Farkas lemma to check if the interval contains a negative certification which shows the nonexistence of solutions in the whole space Rn. Moreover, we will study how to choose a good nonsingular matrix A in the interval operator for P0-matrix linear complementarity problems. We report numerical results to illustrate the efficiency of the proposed technique.
Original languageEnglish
Pages (from-to)15-26
Number of pages12
JournalLinear Algebra and Its Applications
Issue number1-3
Publication statusPublished - 15 Feb 2001
Externally publishedYes


  • Linear complementarity problems
  • Numerical validation
  • P -matrix 0

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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