A New Algorithm Of Positive Definite Quadratic Programming

Quadratic programming is an important area in mathematical programming. Many of the problems can be naturally expressed as quadratic programming problems. This paper compares the advantages and disadvantages of several commonly used algorithms, focuses on a new positive definite quadratic programming algorithm. A detailed theoretical basis and a numerical test for the algorithm are given.First, the quadratic programming model and its present research situation are introduced. The content arrangements of this paper were introduced. The basic knowledge and the basic theory of quadratic programming algorithm are also introduced. This paper gives the existing algorithm for solving the equality quadratic programming and the general quadratic programming are given, and their advantages and disadvantages are compared.Second, the simple numeration algorithm of definite quadratic programming is proposed. The extreme value of proved positive quadratic programming can only be achieved in the vertices, if the value is not in the constraints and also not in the side of the boundary surface and the constrained cross-border online at the boundary surface. The steps of the algorithm and the numerical tests are presented too.Third, using of the geometric significance of positive definite quadratic programming, a new positive definite quadratic programming is made. Related theories are proved, and the numerical tests are presented too. General positive definite quadratic programming problem can be transformed into the objective function norm (distance) in the form. This algorithm gives the method which a general positive definite quadratic programming be transformed into standard form and "normalization"; a new positive definite quadratic programming is constructed. The algorithm for some problems, just make a simple comparison and determination, you can get the optimal solution. For other problems after compare and determine, the optimal solution is got through the simple method iterations. Conducting numerical experiments also confirmed that after the standardization and normalization, it had already completed some of the numerical calculation, the calculation of the follow-up only in reference to the previous results and then performs simple multiplication and division calculations. Numerical experiments show that the algorithm is feasible and effective, and the numerical advantage is significantly better than other algorithms.