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The Linear Complementarity Problem
A revised edition of the standard reference on the linear complementarity problem.
A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems
Following Karmarkar's 1984 linear programming algorithm, numerous interior-point algorithms have been proposed for various mathematical programming problems such as linear programming, convex quadratic programming and convex programming in general. This monograph presents a study of interior-point algorithms for the linear complementarity problem (LCP) which is known as a mathematical model for primal-dual pairs of linear programs and convex quadratic programs. A large family of potential reduction algorithms is presented in a unified way for the class of LCPs where the underlying matrix has nonnegative principal minors (P0-matrix). This class includes various important subclasses such as positive semi-definite matrices, P-matrices, P*-matrices introduced in this monograph, and column sufficient matrices. The family contains not only the usual potential reduction algorithms but also path following algorithms and a damped Newton method for the LCP. The main topics are global convergence, global linear convergence, and the polynomial-time convergence of potential reduction algorithms included in the family.
Complementarity and Variational Problems
After more than three decades of research, the subject of complementarity problems and its numerous extensions has become a well-established and fruitful discipline within mathematical programming and applied mathematics. Sources of these problems are diverse and span numerous areas in engineering, economics, and the sciences. Includes refereed articles.
Some Generalizations of The Linear Complementarity Problem
In this thesis, we study two generalizations of the classical linear complementarity problem (LCP) - the weighted extended linear complementarity problem (wXLCP) and the complementarity problem (CP) over a general closed cone. Our goal is twofold: extend some fundamental results of the LCP to a more general setting and identify a class of nonmonotone problems which could be solved numerically. The thesis is organized as follows: In Chapter 1, we formulate problems relevant to our study and introduce background material that will be needed in the rest of the thesis. In Chapter 2, we formulate the weighted extended linear complementarity problem (XLCP), which naturally generalizes the LCP, the...
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).
Complementarity Problems
The study of complementarity problems is now an interesting mathematical subject with many applications in optimization, game theory, stochastic optimal control, engineering, economics etc. This subject has deep relations with important domains of fundamental mathematics such as fixed point theory, ordered spaces, nonlinear analysis, topological degree, the study of variational inequalities and also with mathematical modeling and numerical analysis. Researchers and graduate students interested in mathematical modeling or nonlinear analysis will find here interesting and fascinating results.
ON SOLVING NEUTROSOPHIC LINEAR COMPLEMENTARITY PROBLEM
The aim of this paper is to propose a methodology for solving Linear Complementarity Problem with Single Valued Trapezoidal Neutrosophic Numbers (SVTN). The effectiveness of the proposed method is illustrated by means of a numerical example. This problem finds many applications in several areas of science, engineering and economics.
Numerical Methods for Linear Complementarity Problems in Physics-Based Animation
Linear complementarity problems (LCPs) have for many years been used in physics-based animation to model contact forces between rigid bodies in contact. More recently, LCPs have found their way into the realm of fluid dynamics. Here, LCPs are used to model boundary conditions with fluid-wall contacts. LCPs have also started to appear in deformable models and granular simulations. There is an increasing need for numerical methods to solve the resulting LCPs with all these new applications. This book provides a numerical foundation for such methods, especially suited for use in computer graphics. This book is mainly intended for a researcher/Ph.D. student/post-doc/professor who wants to study ...
