SIAM Journal on Optimization
Computational Optimization and Applications
Block relaxation and majorization methods for the nearest correlation matrix with factor structure
Computational Optimization and Applications
Solving Log-Determinant Optimization Problems by a Newton-CG Primal Proximal Point Algorithm
SIAM Journal on Optimization
Solving Large-Scale Least Squares Semidefinite Programming by Alternating Direction Methods
SIAM Journal on Matrix Analysis and Applications
A projected semismooth Newton method for problems of calibrating least squares covariance matrix
Operations Research Letters
A Sequential Semismooth Newton Method for the Nearest Low-rank Correlation Matrix Problem
SIAM Journal on Optimization
An inexact spectral bundle method for convex quadratic semidefinite programming
Computational Optimization and Applications
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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.