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二次半定规划的原始对偶内点算法的H..K..M搜索方向的存在唯一性 被引量：4

Existence and Uniquess of H..K..M Search Direction of Primal-Dual Interior Point Algorithm for Quadratic Semtdefinite Programming
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摘要 主要是将半定规划(Semidefinite Programming,简称SDP)的内点算法推广到二次半定规划(Quadratic Semidefinite Programming,简称QSDP),重点讨论了其中搜索方向的产生方法.首先利用Wolfe对偶理论推导得到了求解二次半定规划的非线性方程组,利用牛顿法求解该方程组,得到了求解QSDP的内点算法的H..K..M搜索方向,接着证明了该搜索方向的存在唯一性,最后给出了搜索方向的具体计算方法. This paper extends the interior point algorithm for solving Semidefinite Programming （SDP） to Quadratic Semidefinite Programming（QSDP）, especially discussing the generation of search direction. Firstly, we derive the nonlinear equations for the solution of QSDP using Wolfe＇s dual theorem. The H.. K.. M search direction is got by applying Newton method to the equations. Then we prove the existence and uniqueness of the search direction, and give how to compute H. K. M search direction concretely.
作者 黄静静 王爱文
机构地区 北京信息科技大学理学院
出处 《数学的实践与认识》 CSCD 北大核心 2008年第18期233-238,共6页 Mathematics in Practice and Theory
基金 北京信息科技大学校科研基金(5029323902) 北京市教委科技面上项目(KM200811232009)
关键词 半定规划 二次半定规划 内点算法 搜索方向 牛顿法 semidefinite programming quadratic semidefinite programming interior point algorithm search direction newton method
分类号 O221.2 [理学—运筹学与控制论] O175.1 [理学—基础数学]
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参考文献11

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二级参考文献2

共引文献9

同被引文献24

  • 1徐凤敏,徐成贤.求解二次半定规划的原对偶内点算法(英文)[J].工程数学学报,2006,23(4):590-598. 被引量：4
  • 2Alizadeh F, Haeberly J P, Overton M. Primal dual interior point methods for semidefinite programrning[R]. Technical Report 659, Cumputer Science. New York: New York University, 1994.
  • 3Kojima M, Shindoh S, Hara S. Interior point methods for the monotone semidefinite complementarity promble in symmtric matrices [J ]. SIAM J. Optim. , 1997, 7:86-125.
  • 4Helmberg C, Rendl F, Vanderbei R J, et al. An interior point method for semidefinite programming[J ]. SIAM J. Optim. , 1996,6 : 342-361.
  • 5Monteiro R D C. Primal dual path following algorithms for semidefinite programming[J]. SIAM J. Optim. , 1997,7: 663-678.
  • 6Nesterov Y E,Todd M. Primal dual interior point methods for self scaled cones[J]. SIAM J. Optim. , 1998,8 : 324-364.
  • 7Nesterov Y E, Todd M. Self-scaled barriers and interior point methods for convex programming[J]. Math. Oper. Res. , 1997,22:1-42.
  • 8Xu Fengmin, Xu chengxian. Primal-dual algorithm for quadratic semidefinite programming[J ]. Chinese .lournal of Engineering Mathematics,2006,23 (4) :590-598.
  • 9ZHANG Y. On extending some primal-dual interior-point algorithms from linear programming to semidefinite pro grammning[J ]. SIAM J. Optim. , 1998,8 : 365-386.
  • 10Nesterov Y, Nemirovskii A S. Interior point polynomial methods in convex programming: Theory and algorithms [J ]. SIAM Philadelphia PA. , 1994 : 13.

引证文献4

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数学的实践与认识
2008年 第18期

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