Multiple-Cut Algorithm for Semidefinite Feasibility Problem

史娜; 潘晋孝; 穆学文

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Multiple-Cut Algorithm for Semidefinite Feasibility Problem

更新时间：2026-09-14

- Multiple-Cut Algorithm for Semidefinite Feasibility Problem
- 半定可行性问题的多割算法
- Vol. 31, Issue 6, Pages: 543-547(2010)
- 作者机构：
  
  1. 中北大学理学院
  2. 西安电子科技大学数学系
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2010
- 稿件说明：
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史娜, 潘晋孝, 穆学文. Multiple-Cut Algorithm for Semidefinite Feasibility Problem[J]. 2010, 31(6): 543-547.
DOI：

史娜, 潘晋孝, 穆学文. Multiple-Cut Algorithm for Semidefinite Feasibility Problem[J]. 2010, 31(6): 543-547. DOI：

摘要

半定可行性问题是运筹研究领域中一个很重要的问题.针对此问题提出了一种使用多割的分析中心割平面算法.该算法改进了使用单割的分析中心割平面算法

在解决实际问题时比较有效.通过对该算法收敛性的讨论

证明了该算法是二次收敛的.

Abstract

To solve the semidefinite feasibility problem

it is more efficient to apply the analytic center cutting plane method than to convert it a semidefinite programming problem.A multiple-cut algorithm for the problem was proposed by improving the single-cut algorithm.Its convergence was discussed.The conclusion is proved that it is a quadratic convergent method.

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references

Sun Jie,Kim-Chuan,Zhao Gongyun.An analytic center cutting plane method for semidefinite feasibility problems[J].Mathematic of Operation Research,2002,27(2):332-346.

Boyd S,Ghuoui L E,Feron E,et al.Linear matrix inequalities in system and control theory[M].Philadelphia:SIAM Academic Publishers,1994.

Nesterov Y.Cutting plane algorithms from analytic centers:efficiency estimates[J].Math Programming,1995,69:149-176.

Ye Yinyu.Complexity analysis of the analytic center cutting plane method that uses multiple cuts[J].MathProgramming,1997,78:85-104.

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