Please use this identifier to cite or link to this item: https://doi.org/10.1137/050639831
Title: Computing the nearest doubly stochastic matrix with a prescribed entry
Authors: Bai, Z.-J.
Chu, D. 
Tan, R.C.E. 
Keywords: Doubly stochastic matrix
Generalized Jacobian
Newton's method
Quadratic convergence
Issue Date: 2007
Citation: Bai, Z.-J., Chu, D., Tan, R.C.E. (2007). Computing the nearest doubly stochastic matrix with a prescribed entry. SIAM Journal on Scientific Computing 29 (2) : 635-655. ScholarBank@NUS Repository. https://doi.org/10.1137/050639831
Abstract: 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. © 2007 Society for Industrial and Applied Mathematics.
Source Title: SIAM Journal on Scientific Computing
URI: http://scholarbank.nus.edu.sg/handle/10635/103033
ISSN: 10648275
DOI: 10.1137/050639831
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