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

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  • Zhu, Xiaojing

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.

Suggested Citation

  • Zhu, Xiaojing, 2015. "Computing the nearest low-rank correlation matrix by a simplified SQP algorithm," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 404-414.
    • Handle: RePEc:eee:apmaco:v:256:y:2015:i:c:p:404-414
    DOI: 10.1016/j.amc.2015.01.044
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    1. Alan Brace & Dariusz G¸atarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 127-155, April.
    2. Raoul Pietersz & Patrick Groenen, 2004. "Rank reduction of correlation matrices by majorization," Quantitative Finance, Taylor & Francis Journals, vol. 4(6), pages 649-662.
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