A Semismooth Newton-Type Method for the Nearest Doubly Stochastic Matrix Problem
成果类型：
Article
署名作者：
Hu, Hao; Li, Xinxin; Im, Haesol; Wolkowicz, Henry
署名单位：
Clemson University; University of Waterloo; Jilin University
刊物名称：
MATHEMATICS OF OPERATIONS RESEARCH
ISSN/ISSBN：
0364-765X
DOI：
10.1287/moor.2023.1382
发表日期：
2024
页码：
729-751
关键词：
摘要：
We study a semismooth Newton-type method for the nearest doubly stochastic matrix problem where the nonsingularity of the Jacobian can fail. The optimality conditions for this problem are formulated as a system of strongly semismooth functions. We show that the nonsingularity of the Jacobian does not hold for this system. By exploiting the problem structure, we construct a modified two step semismooth Newton method that guarantees a nonsingular Jacobian matrix at each iteration, and that converges to the nearest doubly stochastic matrix quadratically.