## The Linear Complementarity ProblemDuring the past twenty years, the linear complementarity problem has emerged as an important development in mathematical programming and numerical linear algebra. The Linear Complementarity Problem is a text designed to be suitable for both classroom use and as a references for researchers. The book is ideal for graduate students pursuing an advanced degree in operations research, but it is also of importance for many related fields of study, such as: computer science, applied mathematics, engineering, business studies, etc.* First comprehensive introductory text on the linear complementarity problem (LCP). * Involves all three major aspects on the LCP: theory, applications, and computation. * Text includes numerous exercises to illustrate the theory and computational procedures presented. |

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### Contents

INTRODUCTION | 1 |

BACKGROUND | 43 |

EXISTENCE AND MULTIPLICITY | 137 |

Copyright | |

6 other sections not shown

### Other editions - View all

The Linear Complementarity Problem Richard W. Cottle,Jong-Shi Pang,Richard E. Stone Limited preview - 1992 |

The Linear Complementarity Problem Richard W. Cottle,Jong-Shi Pang,Richard E. Stone Limited preview - 2009 |

### Common terms and phrases

accumulation point affine hull algorithm Applications arbitrary assume assumption augmented LCP basic variables blocking variable bounded computational condition containing q convergence convex copositive Corollary Cottle defined denote distinguished cone driving variable equations equivalent facet feasible follows function given Hence i?nxn implies index set intersection iterative methods LCP q LCP q,M Lemke's method Lemma linear complementarity problem linear programming major cycle MANGASARIAN mapping Mathematical Programming matrix class Newton's method nonbasic nondegenerate nonempty nonlinear complementarity problem nonnegative nonsingular nonzero norm Operations Research optimal orthant P-matrix parametric pivoting method pos C(a pos CM positive definite positive semi-definite principal submatrix Proof Proposition quadratic program result Rnxn row sufficient satisfies scalar scheme Schur complement Section semimonotone sequence SOL(g SOL(q solution of q solution set solves the LCP Step strictly strongly degenerate submatrix subproblem Suppose Theorem theory unique solution variational inequality vector q zero