Computing the nearest low-rank correlation matrix by a simplified SQP algorithm

Xiaojing Zhu

Applied Mathematics and Computation, 2015, vol. 256, issue C, 404-414

Abstract: In this paper, we propose a numerical method for computing the nearest low-rank correlation matrix (LRCM). Motivated by the fact that the nearest LRCM problem can be reformulated as a standard nonlinear equality constrained optimization problem with matrix variables via the Gramian representation, we propose a new algorithm based on the sequential quadratic programming (SQP) method. On each iteration, we do not solve the quadratic program (QP) corresponding to the exact Hessian, but a modified QP with a simpler Hessian. This QP subproblem can be solved efficiently by equivalently transforming it to a sparse linear system. Global convergence is established and preliminary numerical results are presented to demonstrate the proposed method is potentially useful.

Keywords: Low-rank correlation matrix; Matrix optimization; Nonlinear constrained optimization; Gramian representation; Sequential quadratic programming (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:256:y:2015:i:c:p:404-414

DOI: 10.1016/j.amc.2015.01.044

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