A DUAL APPROACH TO SEMIDEFINITE LEAST-SQUARES PROBLEMS

Jérôme Malick 1, *
Abstract : 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.
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SIAM Journal on Matrix Analysis and Applications, Society for Industrial and Applied Mathematics, 2004, 26 (1), pp.272-284
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Jérôme Malick. A DUAL APPROACH TO SEMIDEFINITE LEAST-SQUARES PROBLEMS. SIAM Journal on Matrix Analysis and Applications, Society for Industrial and Applied Mathematics, 2004, 26 (1), pp.272-284. 〈inria-00072409v2〉

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