文档介绍：Subject : A New Algorithm of Positive Definite Quadratic Programming
Specialty : Applied Mathematics
Name : Wang Qian (Signature)
Instructor : Wang Xuefeng (Signature)
ABSTRACT
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 monly 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 pared.
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
programmin