Isotone solutions of parametric linear complementarity problems

Ikuyo Kaneko

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


The parametric linear complementarity problem is given by the conditions:q + αp + Mz ≥ 0, α ≥ 0, z ≥ 0, zT(q + αp + Mz) = 0. Under the assumption that M is a P-matrix, Cottle proved that the solution map z(α) of the above problem is montonically nondecreasing in the parameter α for every nonnegative q and every p if and only if M is a Minkowski matrix. This paper examines whether a similar result holds in various other settings including a nonlinear case.

Original languageEnglish
Pages (from-to)48-59
Number of pages12
JournalMathematical Programming
Issue number1
Publication statusPublished - 1977 Dec 1

ASJC Scopus subject areas

  • Software
  • General Mathematics


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