Gao, Yan; Sun, Defeng Calibrating least squares semidefinite programming with equality and inequality constraints. (English) Zbl 1201.49031 SIAM J. Matrix Anal. Appl. 31(2009), No. 3, 1432-1457 (2010). Summary: 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. Cited in 34 Documents MSC: 49M15 Newton-type methods 49M29 Numerical methods involving duality 90C25 Convex programming 90C30 Nonlinear programming Keywords:covariance matrix; smoothing Newton method; quadratic convergence Software:QSDP; SeDuMi; SDPT3; SDLS; CSDP PDFBibTeX XMLCite \textit{Y. Gao} and \textit{D. Sun}, SIAM J. Matrix Anal. Appl. 31, No. 3, 1432--1457 (2010; Zbl 1201.49031) Full Text: DOI Link