求解大规模带二次简单约束的二次规划的显式自调比投影收缩算法

1　引　　言我们来考虑如下的带二次简单约束的二次规划问题12 x TH x +c Tx =mins.t.,‖ x‖ 2 ≤ a (1)其中 H∈ Rn× n是一个半正定对称矩阵 ,c∈ Rn,这里 a是一个确定的参数 .求解问题 (1)的最基本的方法是构造 L agrange函数 :L (x,λ) =x TH x +2 c Tx +λ(x Tx - a2 ) (2 )当约束起作用时 ,由 x L (x,λ) =0 ,　　 λL (x,λ) =0 ,得H x +c+λx =0‖ x‖ =a (3)即(H +λI) x +c =0‖ x‖ =a从而有‖ (H +λI) - 1 c‖ =a令φ(λ) =‖ (H +λI) - 1 c‖ ,　　 S(λ) =(H +λI) - 1 c则φ2 (λ) =STS =c T(H +λI) - 2 c=…

A SELF-ADAPT PROJECTION CONTRACTION METHOD SOLVING LARGE-SCALE QUADRATIC PROGRAMMING WITH SIMPLE QUADRATIC CONSTRAINT

In this paper, a new self-adapt projection contraction method solving the quadratic programming is established. We give a self-adapt rule for parameter .The solution of the problem is obtained after steady changing parameter . The numerical results show that this algorithm is very effective, especially for large-scale problem, and the precision is improved.