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半定规划的近似中心投影法 被引量：4

A PROJECTIVE METHOD OF THE APPROXIMATE CENTER FOR SEMIDEFINITE PROGRAMMING
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摘要 Many problems in mathematical programming can be modelled as semidefinite programming. The success of interior point algorithms for large-scale linear programming has prompted researchers to develop these algorithms to the semidefinite programming (SDP) case. In this paper, we extend Roos’s projective method for linear programming to SDP. The method is path-following and based on the useof a multiplicative barrier function. The iteration bound depends on the choice ofthe exponent μ in the numerator of the barrier function. The analysis in this paper resembles the one of the approximate center method for linear programming, as proposed by Rocs and Vial [14]. Many problems in mathematical programming can be modelled as semidefinite programming. The success of interior point algorithms for large-scale linear programming has prompted researchers to develop these algorithms to the semidefinite programming (SDP) case. In this paper, we extend Roos's projective method for linear programming to SDP. The method is path-following and based on the useof a multiplicative barrier function. The iteration bound depends on the choice ofthe exponent μ in the numerator of the barrier function. The analysis in this paper resembles the one of the approximate center method for linear programming, as proposed by Rocs and Vial [14].
作者 何炳生
机构地区 南京大学数学系
出处 《计算数学》 CSCD 北大核心 1998年第2期175-176,共2页 Mathematica Numerica Sinica
基金 国家自然科学基金!19671041
关键词 半定规划 近似中心 内点法 近似中心投影法 Semidefinite programming, Approximate center, Interiorpoint method
分类号 O221 [理学—运筹学与控制论]
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参考文献1

  • 1蒋建民，系统科学与数学，1987年，10卷，2期，168页

同被引文献26

  • 1ALIZADEH W F. Interior point methods in semidefinite programming [J]. SIAM Journal on Optimization, 1995, 5 ( 1 ) : 13-51.
  • 2VMDERBERGHE V. Semidefinite programming [J]. SIAM Review, 1996, 38 (1): 49-85.
  • 3FLETCHER R. Semidefinite matrix constraints in optimization[J]. SIAM Journal on Control and Optimization, 1985, 23 (4) :493 - 511.
  • 4HARKER P T, PANG j S. Finite dimensional variational equality and nonlinear complementarity problems: A survey of theory,algorithms, applications [ J ]. Mathematical Programming, 1990, 48 (2): 161-220.
  • 5HE B S. Solving a class of linear projection equations [J]. Numerische Mathematik, 1994, 68 (1): 71-80.
  • 6HE B S. A new method for a class linear variational inequalities [J]. Mathematical Programming, 1994, 66 (2): 137-144.
  • 7Kojima M, Shindoh S, and Hara S. Interior-point methods for the monotone linear complementarity problem in symmetric matrices[J]. SIAM Journal on Optimization, 1997, 7(1): 86-125.
  • 8Kojima M, Shida M, and Shindoh S. Reduction of Monotone Linear Complementarity Problems over Cones to Linear Programs over Cones[J]. Acta Mathematica Vietnamica, 1997,22(1): 147- 157.
  • 9Apkarian P, Noll D, Thevenet J P, et al. A spectral quadratic-SDP method with applications to fixed-order H2 and Hoc synthesis[C]. 2004, 5th Asian Control Conference, Melbourne, Australia.
  • 10Barvinok A L. Problems of distance geometry and convex properties of quadratic maps[J]. Discrete Computational Geometry, 1995, 13(1): 189-202.

引证文献4

二级引证文献5

计算数学
1998年 第2期

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