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The Linear Complementarity Problem
A revised edition of the standard reference on the linear complementarity problem.
The Basic George B. Dantzig
The late George B. Dantzig , widely known as the father of linear programming, was a major influence in mathematics, operations research, and economics. As Professor Emeritus at Stanford University, he continued his decades of research on linear programming and related subjects. Dantzig was awarded eight honorary doctorates, the National Medal of Science, and the John von Neumann Theory Prize from the Institute for Operations Research and the Management Sciences. The 24 chapters of this volume highlight the amazing breadth and enduring influence of Dantzig's research. Short, non-technical summaries at the opening of each major section introduce a specific research area and discuss the current significance of Dantzig's work in that field. Among the topics covered are mathematical statistics, the Simplex Method of linear programming, economic modeling, network optimization, and nonlinear programming. The book also includes a complete bibliography of Dantzig's writings.
Computational Experience with Large-scale Linear Complementarity Problems
This paper contains a brief summary of some computational experience acquired by the Systems Optimization Laboratory at Stanford University on linear complementarity problems of intermediate to large size. (Author).
On Minkowski Matrices and the Linear Complementarity Problem
In this paper, it is shown that the restricted basis simplex method for solving the problem of maximizing the value of a parameter for which a parametric linear complementarity problem with upper bounds on the independent variables is not generally valid. On the positive side, it is shown that a sufficient condition for the method to work is the convexity of a particular art of points. The paper gives necessary and sufficient conditions for this set to be convex.
Solution Rays for a Class of Complementarity Problems
The work deals with the circumstances under which a linear complementarity problem has a ray of complementary solutions emanating from a given complementary solution.
Fundamentals of Quadratic Programming and Linear Complementarity
The fundamental theory and algorithms of quadratic programming and linear complementarity are presented in expository form. Computational experience is reviewed. (Author).
Linear and Nonlinear Optimization
This textbook on Linear and Nonlinear Optimization is intended for graduate and advanced undergraduate students in operations research and related fields. It is both literate and mathematically strong, yet requires no prior course in optimization. As suggested by its title, the book is divided into two parts covering in their individual chapters LP Models and Applications; Linear Equations and Inequalities; The Simplex Algorithm; Simplex Algorithm Continued; Duality and the Dual Simplex Algorithm; Postoptimality Analyses; Computational Considerations; Nonlinear (NLP) Models and Applications; Unconstrained Optimization; Descent Methods; Optimality Conditions; Problems with Linear Constrain...
