A field guide to the matrix classes found in the literature of the linear complementarity problem

Authors:
Richard W. Cottle
Affiliations:
Stanford University, Stanford, USA
Venue:
Journal of Global Optimization
Year:
2010

Citing 4
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The basic theorem of complementarity revisited

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Think co(mpletely)positive ! Matrix properties, examples and a clustered bibliography on copositive optimization

Journal of Global Optimization

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Abstract

There are more than 50 matrix classes discussed in the literature of the Linear Complementarity Problem. This guide is offered as a compendium of notations, definitions, names, source information, and commentary on these many matrix classes. Also included are discussions of certain properties possessed by some (but not all) of the matrix classes considered in this guide. These properties--fullness, completeness, reflectiveness, and sign-change invariance--are the subject of another table featuring matrix classes that have one or more of them. Still another feature of this work is a matrix class inclusion map depicting relationships among the matrix classes listed herein.