| 半定优化与半光滑牛顿算法 |
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| 引用本文： | 孙捷.半定优化与半光滑牛顿算法[J].运筹学学报,2004,8(1):41-52. |
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| 作者姓名： | 孙捷 |
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| 作者单位： | SchoolofBusiness,NationalUniversityofSingapore,RepublicofSingapore |
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| 基金项目： | This work was supported in part by Singapore-MIT Alliance，Grants RP314000-028/042-112 of National University of Singapore. |
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| 摘 要： | 本文讨论半光滑牛顿算法的基本概念与其在求解半定优化问题中的应用．特别地，该算法可用于求解线性或非线性半定互补问题．本文同时综述最近在矩阵方程，增广拉格朗日公式和半定优化稳定性方面的、源于半光滑牛顿算法的理论成果．
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| 关 键 词： | 半定优化 半光滑牛顿算法 变分不等式 矩阵方程 拉格朗日公式 |
Semidefinite Optimization and Semismooth Newton's Method |
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| Abstract.Semidefinite Optimization and Semismooth Newton''''s Method[J].OR Transactions,2004,8(1):41-52. |
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| Authors: | Abstract |
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| Abstract: | We discuss basic ideas of a semismooth Newton's method and its application in solving semideflnite optimization (SDO) problems. In particular, the method can be used to solve both linear and nonlinear semidefinite complementarity problems. We also survey recent theoretical results in matrix functions, augmented Lagrangian, and stability of SDO that stem from the research on the matrix form of nonsmooth Newton's methods. |
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| Keywords: | Operations Research semismooth functions semidefinite optimization Newton's method complementarity problems stability variational inequality |
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