Monotone solutions of the parametric linear complementarity problem

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 1972 English Publisher:Springer Science and Business Media LLCJournal:Mathematical Programming, volume 3-3, pages 210-224 (issn: 0025-5610, eissn: 1436-4646,

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Authors: Richard W. Cottle;

doi: 10.1007/bf01584990

Monotone solutions of the parametric linear complementarity problem

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Abstract

The parametric linear complementarity problem under study here is given by the conditionsq + αp + Mz ≥ 0,α ≥ 0,z ≥ 0,z T (q + αp + Mz) = 0 whereq is nonnegative. This paper answers three questions including the following one raised by G. Maier: What are the necessary and sufficient conditions onM guaranteeing that for every nonnegative starting pointq and every directionp the components of the solution to the parametric linear complementarity problem are nondecreasing functions of the parameterα?

Related Organizations

Stanford University
United States

Keywords

Quadratic programming

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