In this paper, we propose a modified mean-variance portfolio selection procedure using the proximal gradient method. This novel selection procedure has the advantage of encouraging sparsity in the entire portfolio usingl0−norm while requiring only O(n) storage. The proximal gradient method (PSG) introduces a multiple damping gradient (MDG) method to reduce the computation time, with Lipschitz constant serving as the step size, and iterative thresholding (IHT) as the proximal method to induce the sparsity of the portfolio. To find the optimal portfolio, an efficient algorithm is developed. The performance of the proposed selection procedure is illustrated by its application to real-life data set. It is shown that the proposed portfolio performs consistently better in comparison with other methods.

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