Necessary And Sufficient Conditions For The Existence Of Complementary Solutions And Characterizations Of The Matrix Classes Q And Qo
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Topological Methods in Complementarity Theory
Author: G. Isac
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-04-17
Complementarity theory is a new domain in applied mathematics and is concerned with the study of complementarity problems. These problems represent a wide class of mathematical models related to optimization, game theory, economic engineering, mechanics, fluid mechanics, stochastic optimal control etc. The book is dedicated to the study of nonlinear complementarity problems by topological methods. Audience: Mathematicians, engineers, economists, specialists working in operations research and anybody interested in applied mathematics or in mathematical modeling.
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Necessary and Sufficient Conditions for the Existence of Complementary Solutions and Characterizations of the Matrix Classes Q and QO.
The linear complementarity problem has a solution if and only if there exists a right-hand-side vector of an associated dual linear program such that at least one LP solution falls inside a specific open set. This condition is used to given different characterizations of the matrix classes Q and Q sub O. Moreover, they are used to derive verifiable sufficient conditions for a subclass of Q. Keywords: Linear Complementarity Problem, Q-Matrices, Q sub O matrices.