一个解凸二次规划的预测-校正光滑化方法

张菊亮;章祥荪

系统科学与数学 ›› 2003, Vol. 23 ›› Issue (3) : 353-366.

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PDF(529 KB)
系统科学与数学 ›› 2003, Vol. 23 ›› Issue (3) : 353-366. DOI: 10.12341/jssms09600
论文

一个解凸二次规划的预测-校正光滑化方法

    张菊亮(1),章祥荪(2)
作者信息 +

A PREDICTOR-CORRECTOR METHOD FOR CONVEX QUADRATIC PROGRAMMING

    Ju Lian ZHANG(1),Xiang Sun ZHANG(2)
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摘要

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.

Abstract

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.

关键词

二次规划 / 全局收敛性 / 预测-校正光滑化方法 /

Key words

Quadratic programming / global convergence / predictor-corrector smoothing method / quadratic convergen

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张菊亮 , 章祥荪. 一个解凸二次规划的预测-校正光滑化方法. 系统科学与数学, 2003, 23(3): 353-366. https://doi.org/10.12341/jssms09600
Ju Lian ZHANG , Xiang Sun ZHANG. A PREDICTOR-CORRECTOR METHOD FOR CONVEX QUADRATIC PROGRAMMING. Journal of Systems Science and Mathematical Sciences, 2003, 23(3): 353-366 https://doi.org/10.12341/jssms09600
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