The Existence Conditions Of Solution Of The Linear Complementarity Problem

The core of this topic, which was studied the existent of the value and the property of the linear complementary problems. This paper consists of three section s,firstly, introduced the linear complementarity problem, secondly, after optimized th e linear complementarity problems, we obtained the property of the CLP, eventually, we summarized the different forms of the existence of the linear complementary problem solutions promotion, tand other properties. Under the joint efforts of the scholars in all walks of life, we believe more and more properties of the solution of the linearcomplementary problems will be unearth. These properties will provide a better proper environment for the new algorithm research derivatives than before, and catching a powerful role in promoting.The main innovative results of this paper are as follows:1. With the help of former scholar’s results, and by using the method of the quadratic optimization, so the horizontal linear complementarity problem is equally transformed into a quadratic optimization problem which optimal value is 0. Base on that, I explored properties of solves of the linear complementatity problem.2. This paper has proved that the solution set of the generalized linear complementarity problem is convexity, and the property of KKT point.3. After further studied the solution of the existence of the horizontal linear complementarity problem and other properties, and the nature of the solution set of generalized linear complementarity problem, we have explored the existence of the solutions and uniqueness properties of the settlement, which was the properties of the existence of mixed linear complementarity problem.