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In this paper, we consider the generalized low rank approximation of thecorrelation matrices problem which arises in the asset portfolio. We firstcharacterize the feasible set by using the Gramian representation together witha special trigonometric function transform, and then transform the generalizedlow rank approximation of the correlation matrices problem into anunconstrained optimization problem. Finally, we use the conjugate gradientalgorithm with the strong Wolfe line search to solve the unconstrainedoptimization problem. Numerical examples show that our new method is feasibleand effective.

On the generalized low rank approximation of the correlation matrices arising in the asset portfolio