Computer Science and Scientific Computing
3 total works
This book provides a comprehensive treatment of the theory of matrix polynomials. The theory developed here is a natural extension to polynomials of higher degrees, and forms an important new part of linear algebra for which the main concepts and results have been arrived at during the past five years.
The Linear Complementarity Problem
by Richard W. Cottle, etc., Jong-Shi Pang, and Richard E. Stone
Published 4 February 1992
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.
This book treats the fundamental issues and algorithmic strategies emerging as the core of the discipline of discrete optimization in a comprehensive and rigorous fashion. Following an introductory chapter on computational complexity, the basic algorithmic results for the two major models of polynomial algorithms are introduced--models using matroids and linear programming. Further chapters treat the major non-polynomial algorithms: branch-and-bound and cutting planes. The text concludes with a chapter on heuristic algorithms.Several appendixes are included which review the fundamental ideas of linear programming, graph theory, and combinatorics--prerequisites for readers of the text. Numerous exercises are included at the end of each chapter.