A multidimensional scaling approach for representing XML documents
ACM-SE 45 Proceedings of the 45th annual southeast regional conference
Correlation stress testing for value-at-risk: an unconstrained convex optimization approach
Computational Optimization and Applications
Computers & Mathematics with Applications
Design of recurrent neural networks for solving constrained least absolute deviation problems
IEEE Transactions on Neural Networks
Calibrating Least Squares Semidefinite Programming with Equality and Inequality Constraints
SIAM Journal on Matrix Analysis and Applications
Block relaxation and majorization methods for the nearest correlation matrix with factor structure
Computational Optimization and Applications
Solving Large-Scale Least Squares Semidefinite Programming by Alternating Direction Methods
SIAM Journal on Matrix Analysis and Applications
Dual approaches to finite element model updating
Journal of Computational and Applied Mathematics
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
Geometric multiscale decompositions of dynamic low-rank matrices
Computer Aided Geometric Design
Approximation of rank function and its application to the nearest low-rank correlation matrix
Journal of Global Optimization
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In this paper, we study the projection onto the intersection of an affine subspace and a convex set and provide a particular treatment for the cone of positive semidefinite matrices. Among applications of this problem is the calibration of covariance matrices. We propose a Lagrangian dualization of this least-squares problem, which leads us to a convex differentiable dual problem. We propose to solve the latter problem with a quasi-Newton algorithm. We assess this approach with numerical experiments which show that fairly large problems can be solved efficiently.