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|Title:||Calibrating least squares semidefinite programming with equality and inequality constraints|
Smoothing Newton method
|Source:||Gao, Y., Sun, D. (2009). Calibrating least squares semidefinite programming with equality and inequality constraints. SIAM Journal on Matrix Analysis and Applications 31 (3) : 1432-1457. ScholarBank@NUS Repository. https://doi.org/10.1137/080727075|
|Abstract:||In this paper, we consider the least squares semidefinite programming with a large number of equality and inequality constraints. One difficulty in finding an efficient method for solving this problem is due to the presence of the inequality constraints. In this paper, we propose to overcome this difficulty by reformulating the problem as a system of semismooth equations with two level metric projection operators. We then design an inexact smoothing Newton method to solve the resulting semismooth system. At each iteration, we use the BiCGStab iterative solver to obtain an approximate solution to the generated smoothing Newton linear system. Our numerical experiments confirm the high efficiency of the proposed method. © 2009 Society for Industrial and Applied Mathematics.|
|Source Title:||SIAM Journal on Matrix Analysis and Applications|
|Appears in Collections:||Staff Publications|
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