A Modified Active-Set Algorithm For Quadratic Programming

Quadratic programming is a kind of simplest and most prime non-linear programming problem.It have be very important significance to study algorithm for quadratic programming,due to its particularity and the solution of non-linear programming can be transformed to solve a series of quadratic programming problems by means of quadratic approximation.The theme of this paper is the exploration of algorithm for quadratic programming.In chapter 1,we introduced some basic conception concerned with nonlinear programming such as gradient,Hessian matrix,convex set, convex function,Taylor expansion,descent direction and feasible direction, etc.In chapter 2,we offered a modified algorithm for quadratic programming problem.The modification include two aspects,on the one hand we introduced a method of descent in the process of solving quadratic programming subproblems with equality constraints which owe to a new approach of optimization advanced by professor Z.M.Li,on the other hand we modified the direction of search,namely regarded gradient-project direction as the direction of search while(?)~k≠x~k.The final aim of those modifications is to reduce the degrees of iteration and improve the efficiency of operation.As approved by examples and the confirmation of convergence,the modified algorithm for quadratic programming is more effeative and more ascendant.