The Linear Complementarity Problem And Equivalent Problems

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The Linear Complementarity Problem And Equivalent Problems

The Linear Complementarity Problem And Equivalent Problems written by Narayanaswamy Nagarajan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Linear complementarity problem categories.

The Linear Complementarity Problem

The Linear Complementarity Problem written by Richard Cottle and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Business & Economics categories.

During 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.

Geometric Aspects Of The Linear Complementarity Problem

Geometric Aspects Of The Linear Complementarity Problem written by Richard E. Stone and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Linear complementarity problem categories.

A large part of the study of the Linear Complementarity Problem (LCP) has been concerned with matrix classes. A classic result of Samelson, Thrall, and Wesler is that the real square matrices with positive principal minors (P-matrices) are exactly those matrices M for which the LCP (q, M) has a unique solution for all real vectors q. Taking this geometrical characterization of the P-matrices and weakening, in an appropriate manner, some of the conditions, we obtain and study other useful and broad matrix classes thus enhancing our understanding of the LCP. In Chapter 2, we consider a generalization of the P-matrices by defining the class U as all real square matrices M where, if for all vectors x within some open ball around the vector q the LCP (x, M) has a solution, then (q, M) has a unique solution. We develop a characterization of U along with more specialized conditions on a matrix for sufficiency or necessity of being in U. Chapter 3 is concerned with the introduction and characterization of the class INS. The class INS is a generalization of U gotten by requiring that the appropriate LCP's (q, M) have exactly k solutions, for some positive integer k depending only on M. Hence, U is exactly those matrices belonging to INS with k equal to one. Chapter 4 continues the study of the matrices in INS. The range of values for k, the set of q where (q, M) does not have k solutions, and the multiple partitioning structure of the complementary cones associated with the problem are central topics discussed. Chapter 5 discusses these new classes in light of known LCP theory, and reviews its better known matrix classes. Chapter 6 considers some problems which remain open. (author).

Sufficient Matrices And The Linear Complementarity Problem

Sufficient Matrices And The Linear Complementarity Problem written by R. W. Cottle and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Linear complementarity problem categories.

Abstract: "In this paper we pose and answer two questions about solutions of the linear complementarity problem (LCP). The first question is concerned with the conditions on a square matrix M which quarantee that for every vector q, the solutions of LCP (q, M) are identical to the Karush-Kuhn-Tucker points of the natural quadratic program associated with (q, M). In answering this question we introduce the class of 'row sufficient' matrices. The transpose of such a matrix is what we call 'column sufficient.' The latter matrices turn out to furnish the answer to our second question which asks for the conditions on M under which the solution set of (q, M) is convex for every q. In addition to these two main results, we discuss the connections of these two new matrix classes with other well-known matrix classes in linear complementarity theory."

The Linear Complementarity Problem

The Linear Complementarity Problem written by Richard W. Cottle and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-27 with Mathematics categories.

A revised edition of the standard reference on the linear complementarity problem.

Siam Journal On Control And Optimization

Siam Journal On Control And Optimization written by Society for Industrial and Applied Mathematics and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Control theory categories.

Siam Journal On Matrix Analysis And Applications

Siam Journal On Matrix Analysis And Applications written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.

Oriented Matroids And The Linear Complementarity Problem

Oriented Matroids And The Linear Complementarity Problem written by Walter Duff Morris and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Linear complementarity problem categories.

Journal Of Nonlinear And Convex Analysis

Journal Of Nonlinear And Convex Analysis written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Convex domains categories.

Mathematics Of Operations Research

Mathematics Of Operations Research written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.

Articles of mathematical interest as well as operations research and management science.