Computing the Nearest Doubly Stochastic Matrix with A Prescribed Entry
Computing the Nearest Doubly Stochastic Matrix with A Prescribed Entry
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DOI：
10.1137/050639831
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发表时间：
2007-03
期刊：
影响因子：
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通讯作者：
Zhengjian Bai;D. Chu;R. C. Tan
中科院分区：
文献类型：
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作者：
Zhengjian Bai;D. Chu;R. C. Tan
本文研究了一类最近邻双随机矩阵问题。这个问题是找到与给定矩阵最接近的具有指定$(1,1)$条目的双随机矩阵。根据优化中的对偶理论，该问题的对偶是一个无约束可微的，但不是二次可微的凸优化问题。采用牛顿型方法求解相关的对偶问题，得到最近邻的双随机矩阵。在一些温和的假设条件下，证明了牛顿方法的二次收敛性。通过数值算例验证了该方法的数值性能。
In this paper a nearest doubly stochastic matrix problem is studied. This problem is to find the closest doubly stochastic matrix with the prescribed $(1,1)$ entry to a given matrix. According to the well-established dual theory in optimization, the dual of the underlying problem is an unconstrained differentiable, but not twice differentiable, convex optimization problem. A Newton-type method is used for solving the associated dual problem, and then the desired nearest doubly stochastic matrix is obtained. Under some mild assumptions, the quadratic convergence of the proposed Newton method is proved. The numerical performance of the method is also demonstrated by numerical examples.