Equivalence Between Different Formulations of the Linear Complementarity Problem

Mihai Anitescu; Goran Lesaja; Florian A. Potra

doi:10.1080/10556789708805657

Equivalence Between Different Formulations of the Linear Complementarity Problem

Mihai Anitescu
, Goran Lesaja
, Florian A. Potra

Mathematical Sciences

University of Iowa

Research output: Contribution to journal › Article › peer-review

37 Scopus citations

Abstract

One shows that different formulations of the linear complementarity problem (LCP), such as the horizontal LCP, the mixed LCP and the geometric LCP can be transformed into a standard LCP. The P_*(κ)-property (a more general property than monotonicity) of the corresponding formulations as well as the convergence properties of a large class of interior-point algorithms are invariant with respect to the transformations. Therefore it is sufficient to study the algorithms only for the standard LCP.

Original language	American English
Journal	Optimization Methods and Software
Volume	7
DOIs	https://doi.org/10.1080/10556789708805657
State	Published - Jan 1 1997

Disciplines

Education
Mathematics

Keywords

Equivalence
Infeasible-Interior-Point Algorithm
Linear Complementarity Problem
P*Matrices
Polynomiality
Quadratic Convergence

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https://doi.org/10.1080/10556789708805657

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title = "Equivalence Between Different Formulations of the Linear Complementarity Problem",

abstract = "One shows that different formulations of the linear complementarity problem (LCP), such as the horizontal LCP, the mixed LCP and the geometric LCP can be transformed into a standard LCP. The P*(κ)-property (a more general property than monotonicity) of the corresponding formulations as well as the convergence properties of a large class of interior-point algorithms are invariant with respect to the transformations. Therefore it is sufficient to study the algorithms only for the standard LCP.",

keywords = "Equivalence, Infeasible-Interior-Point Algorithm, Linear Complementarity Problem, P*Matrices, Polynomiality, Quadratic Convergence",

author = "Mihai Anitescu and Goran Lesaja and Potra, \{Florian A.\}",

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T1 - Equivalence Between Different Formulations of the Linear Complementarity Problem

AU - Anitescu, Mihai

AU - Lesaja, Goran

AU - Potra, Florian A.

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Y1 - 1997/1/1

N2 - One shows that different formulations of the linear complementarity problem (LCP), such as the horizontal LCP, the mixed LCP and the geometric LCP can be transformed into a standard LCP. The P*(κ)-property (a more general property than monotonicity) of the corresponding formulations as well as the convergence properties of a large class of interior-point algorithms are invariant with respect to the transformations. Therefore it is sufficient to study the algorithms only for the standard LCP.

AB - One shows that different formulations of the linear complementarity problem (LCP), such as the horizontal LCP, the mixed LCP and the geometric LCP can be transformed into a standard LCP. The P*(κ)-property (a more general property than monotonicity) of the corresponding formulations as well as the convergence properties of a large class of interior-point algorithms are invariant with respect to the transformations. Therefore it is sufficient to study the algorithms only for the standard LCP.

KW - Equivalence

KW - Infeasible-Interior-Point Algorithm

KW - Linear Complementarity Problem

KW - PMatrices

KW - Polynomiality

KW - Quadratic Convergence

UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/580

UR - https://doi.org/10.1080/10556789708805657

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M3 - Article

SN - 1055-6788

VL - 7

JO - Optimization Methods and Software

JF - Optimization Methods and Software

ER -

Equivalence Between Different Formulations of the Linear Complementarity Problem

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