The Research On The Algorithms Of Some Quadratic Programming

This thesis deals with the topic of algorithms of some Quadratic Programming problems. Quadric Programming is a very important and active branch in operation research, Researching the algorithms of Quadratic Programming is not only to solve it but also to solve other nonlinear programmings. Because most optimization algorithms are educed from Quadratic Programming.This kind of methods are efficiency in practice, mostly because many functions are closed to quadratic function at the minimum points and it is NP hard.In Chaper1, after introducing some basic concepts and properties of Quadratic Programming, we give a brief overview of main obtained results in the thesis.In Chapter 2, we presented a decomposition iterative algorithm for solving genenal Quadraic Programming problems. We proved that the sequence solutions generated by the algorithm converges to the optimal solution of the original problem, and has a linear rate of convergence if the Hessian matrix H is positive definite, or to a stationary point if the matrix H is indefinite.In Chapter 3, we discussed a dual algorithm for minimizing the convex Quaduatic Programming with box constraints. The algorithm avoids computing generalized inverse matrix, and we give an example to show that this algorithm is efficient.In Chapter 4. we transfered the portfolio coefficient problem into an equivalent unconstrained problem when it is a positive definite Quadratic Programming. Moreover, we got the relationship between the K-T point of the primal problem and the stationary point of the unconstrained problem. This method provided some scientific evidence and an algorithm to the optimal portfolio investment.We conclude the thesis in chapter 5 by proposing some problems for further research on the algorithms of the Quadratic Programming.