| 张宏伟,贾红,陈爽,庞丽萍.求解随机二阶锥线性互补问题的期望残差最小化方法[J].,2015,55(4):431-435 |
| 求解随机二阶锥线性互补问题的期望残差最小化方法 |
| ERM method for stochastic linear complementarity problem solution of the second-order cone |
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| DOI：10.7511/dllgxb201504015 |
| 中文关键词: 随机二阶锥线性互补问题 期望残差最小化(ERM)方法 若尔当积 谱分解 |
| 英文关键词: stochastic linear complementarity problem of the second-order cone expected residual minimization (ERM) method Jordan algebra spectral factorization |
| 基金项目:国家自然科学基金资助项目(91330206). |
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| 摘要点击次数: 1471 |
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| 中文摘要: |
| 引入期望残差最小化(ERM)方法来求解随机二阶锥线性互补问题．在非负象限内，利用ERM方法求解随机线性互补问题是可行的，为此将非负象限内的随机线性互补问题延伸到二阶锥内．首先，介绍了二阶锥矢量相关的若尔当积及谱分解等预备知识．然后，通过二阶锥互补函数FB函数将随机二阶锥线性互补问题转化为极小化问题．以预备知识为基础证明了若尔当积下的x 2与x 2的关系，并进一步证明了离散型目标函数解的存在性与收敛性．最后，证明利用ERM方法解随机二阶锥互补问题是可行的． |
| 英文摘要: |
| Expected residual minimization (ERM) method is introduced to solve the stochastic linear complementarity problem of the second-order cone. It has been testified that it is feasible to use ERM method to solve stochastic linear complementarity problem in non-negative quadrant. This method will be extended to the second-order cones. To begin with, some basic knowledge and properties of Jordan algebra and the spectral factorization of vectors associated with the second-order cone are presented. Then, through the second-order cone complementarity function, that is FB function, the stochastic linear complementarity problem of the second-order cone is transformed to be a minimizing problem. The relationship between x 2 and x 2 under the Jordan algebra based on the basic knowledge is proved. Furthermore, the existence and convergence of the solution set of discrete objective function are proved. Finally, a conclusion is drawn that it is feasible to solve the stochastic linear complementarity problem of the second-order cone by using ERM method. |
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