On the generalized low rank approximation of the correlation matrices arising in the asset portfolio
This work addresses a computational problem in financial portfolio optimization, but the contribution is incremental as it applies existing optimization techniques to a specific matrix approximation formulation.
The authors propose a method for generalized low-rank approximation of correlation matrices in asset portfolio optimization, transforming it into an unconstrained problem solved via conjugate gradient with strong Wolfe line search. Numerical examples demonstrate feasibility and effectiveness.
In this paper, we consider the generalized low rank approximation of the correlation matrices problem which arises in the asset portfolio. We first characterize the feasible set by using the Gramian representation together with a special trigonometric function transform, and then transform the generalized low rank approximation of the correlation matrices problem into an unconstrained optimization problem. Finally, we use the conjugate gradient algorithm with the strong Wolfe line search to solve the unconstrained optimization problem. Numerical examples show that our new method is feasible and effective.