求解凸规划问题的一种新的连续化方法

辽宁石油化工大学学报 ›› 2006, Vol. 26 ›› Issue (1): 91-93.

求解凸规划问题的一种新的连续化方法

路永洁, 宋岱才

LU Yong -jie , SONG Dai -cai

收稿日期:2005-10-18 出版日期:2006-01-25 发布日期:2006-01-25
作者简介:路永洁(1964 -), 女, 江苏宜兴市, 副教授, 硕士。
基金资助:
辽宁石油化工大学重点学科建设资助项目(K200409)。

A New Cont inuous Method for Solving Convex Prog ramming Problems

School of Science , Liaoning University of Petroleum & Chemical Technology , Fushun Liaoning 113001, P .R .China

Received:2005-10-18 Published:2006-01-25 Online:2006-01-25

摘要/Abstract

摘要： 　对于凸规划问题min f(x), s .t .gi(x)≤0(i =1 , 2, … , m), 其中, x ∈ Rn ;f(x), gi(x):R n ※R 为二次连续可微凸函数。利用Fischer 提出的一类新的凸规划问题等价条件, 给出了一个解此问题新的连续化方法。通过路径追踪求解New ton 类同伦方程, 得到凸规划问题的K -K -T 点, 从而得到凸规划问题的解, 并且证明了方法的全局收敛性。最后举例验证了方法的正确性。

关键词: 　凸规划, 　等价条件, 　同伦方程, 　全局收敛

Abstract:

　Consider the convex programming problems min f (x ), s .t .gi(x )≤0(i =1 , 2 , … , m), w here x ∈ Rn and f(x), gi(x):R n ※ R are twice continuously differentiable convex function .Based on a new class equivalent condition of convex programming problems, which was first presented by Fischer , a new continuous method was put forward to solve the problem .K -K -T points of convex programming were found by path computing New ton homotopy equation, and the convex programming problems were solved.Its global convergence was proved.Finally , the method was validated with example.

Key words: 　Convex programming , 　Equivalent condition, 　Homo topy equation , 　Global convergence

路永洁, 宋岱才. 求解凸规划问题的一种新的连续化方法[J]. 辽宁石油化工大学学报, 2006, 26(1): 91-93.

LU Yong -jie,SONG Dai -cai. A New Cont inuous Method for Solving Convex Prog ramming Problems[J]. Journal of Liaoning Petrochemical University, 2006, 26(1): 91-93.