一类线性与框式约束凸规划问题的原始-对偶内点算法

运筹与管理 ›› 2013, Vol. 22 ›› Issue (6): 39-44.

一类线性与框式约束凸规划问题的原始-对偶内点算法

张艺

宁波大学理学院,浙江宁波 315211

收稿日期:2011-12-21 出版日期:2013-12-25
作者简介:张艺(1960-),男,副教授,主要研究方向:最优化理论与计算、数值代数。
基金资助:
宁波大学学科科研资金资助项目(xkl060);浙江省海洋与渔业资金资助项目(ZHYF201102);浙江省教育厅科研资金资助项目 (Y201119382)

A Primal-dual Interior Point Algorithm for a Class of Convex Programming Problem with Linear and Box Constraints

ZHANG Yi

Faculty of Science, Ningbo University, Ningbo 315211, China

Received:2011-12-21 Online:2013-12-25

摘要/Abstract

摘要： 本文对一类具有线性和框式约束的凸规划问题给出了一个原始-对偶内点算法, 该算法可在任一原始-对偶可行内点启动, 并且全局收敛,当初始点靠近中心路径时, 算法成为中心路径跟踪算法。数值实验表明, 算法对求解大型的这类问题是有效的。

关键词: 凸规划, 内点算法, 原始-对偶, 路径跟踪

Abstract: In this paper, we present a primal-dual interior point algorithm for a class of convex programming problem with linear and box constrains. The algorithm can be started at any primal-dual feasible interior point and admits the global convergence. When the initial point is close to the central path, it becomes a central path-following algorithm. Numerical experiments show the proposed algorithm is effective for the large scale problems.

Key words: convex programming, interior point algorithm, primal-dual, path-following

中图分类号:

O221.2

张艺. 一类线性与框式约束凸规划问题的原始-对偶内点算法[J]. 运筹与管理, 2013, 22(6): 39-44.

ZHANG Yi. A Primal-dual Interior Point Algorithm for a Class of Convex Programming Problem with Linear and Box Constraints[J]. Operations Research and Management Science, 2013, 22(6): 39-44.