一个解凸二次规划的预测-校正光滑化方法

A PREDICTOR-CORRECTOR METHOD FOR CONVEX QUADRATIC PROGRAMMING

本文为凸二次规划问题提出一个光滑型方法,它是Engelke和Kanzow提出的解线性规划的光滑化算法的推广。其主要思想是将二次规划的最优性K-T条件写成一个非线性非光滑方程组,并利用Newton型方法来解其光滑近似。本文的方法是预测-校正方法。在较弱的条件下,证明了算法的全局收敛性和超线性收敛性。

In this paper, a smoothing method, which is a generalization of Engelke and Kanzow's smoothing method for linear programming, is presented for convex quadratic programming. The main idea is to convert the K-T condition of the quadratic programming to a system of nonlinear nonsmooth equations. And then we apply Newton-type method to solve its smoothing approximation. Our method is a predictor-corrector method. The global and superlinear convergence of the method is obtained under very mild conditions.