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A feasible filter method for the nearest low-rank correlation matrix problem

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Abstract

The nearest low-rank correlation matrix problem plays an important role in mathematical finance. This problem is challenging because of its complicated nonconvex constraints. Preserving the constraints in traditional algorithms for this problem is numerically expensive. In this paper, we present a new easily computed constraint-preserving update scheme which can be viewed as a generalization of the Cayley transform, a classical retraction on the Stiefel manifold. A simple filter mechanism for unconstrained optimization is used in our feasible method to promote global convergence to first-order critical points. Numerical results demonstrate the potential efficiency of the proposed method.

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Authors and Affiliations

  1. School of Mathematics and Physics, Shanghai University of Electric Power, Shanghai, 200090, People’s Republic of China

    Xiaojing Zhu

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  1. Xiaojing Zhu
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Correspondence to Xiaojing Zhu.

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Zhu, X. A feasible filter method for the nearest low-rank correlation matrix problem. Numer Algor 69, 763–784 (2015). https://doi.org/10.1007/s11075-014-9924-y

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  • DOI: https://doi.org/10.1007/s11075-014-9924-y

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