A Semismooth Newton-Type Method for the Nearest Doubly Stochastic Matrix Problem

Hao Hu (), Xinxin Li (), Haesol Im () and Henry Wolkowicz ()
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Hao Hu: School of Mathematical and Statistical Sciences, Clemson University, Clemson, South Carolina 29634; Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
Xinxin Li: School of Mathematics, Jilin University, Changchun 130012, China
Haesol Im: Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
Henry Wolkowicz: Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

Mathematics of Operations Research, 2024, vol. 49, issue 2, 729-751

Abstract: 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.

Keywords: 90C20; 90C25; 90C33; 90C46; 49M15; nearest doubly stochastic matrix; semismooth Newton method; strongly semismooth; quadratic convergence; equivalence class (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:49:y:2024:i:2:p:729-751

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