Based On The Distance Of The Positive Definite Quadratic Programming Algorithm

Quadratic programming is an important content in mathematical programming. It hasbeen applied more broadly in many fields, such as Operations Research, Economicmathematics and so on. So it has a very important significance to research the algorithm ofthe quadratic programming. The paper introduces the quadratic programming model and thebasic theory. Also give a brief review on the current status of the quadratic programming. Thearticle state the solving measures of equality quadratic programming and the general quadraticprogramming, then makes a comparison between them to explain the advantages anddisadvantages. And also the paper analyze the objective function of the positive definitequadratic programming. According to the geometric significance of the positive definitequadratic programming, proof the optimal solution exist in the feasible region border ororigin.Based on the geometric significance of positive definite quadratic programming, thepaper came up the new algorithm according to the distance of the distance of the positivedefinite quadratic programming algorithm. The thought of the new algorithm that is calculatethe projective point. The projective point is the origin to the straight line or plane. The paperalso proposed the computing method to solve the projective point. In fact, this process alsoget optimal solution. In traditional algorithm, it is need to work out the inverse of a matrix inthe process of the calculate projective point. But in the new method, it do some improvedmeasures. The matrix inverse started from one-dimensional. After the judgment andcomparison, to decide whether or not to calculate the matrix inverse of two-dimensional,again judgment and comparison until find optimal solutions. It started with the simple inverseof a matrix.Then decide whether or not to calculate the much higher levels of the matrixinverse after the judgment. In addition, the paper do some relevant theoretical proof andnumerical testing. And also do some comparison with active set method, allelomorph method,Zoutendijk method, quadprog function. The numerical test results shows that the new algorithm can avoid lot of repeated computation, reduce the compute capacity and saveresources.