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    Area of Science:

    • Quantitative Finance
    • Optimization Theory
    • Computational Finance

    Background:

    • The Markowitz mean-variance model is widely used in portfolio optimization.
    • Sparse regularization is popular for achieving sparse portfolios.
    • Existing penalty-based methods lack explicit control over portfolio size (cardinality).

    Purpose of the Study:

    • To reformulate the mean-variance model as a cardinality-constrained nonconvex optimization problem.
    • To develop an algorithm that explicitly controls the number of assets in a portfolio.
    • To address the limitation of regularization parameter dependency in existing methods.

    Main Methods:

    • Formulation of the mean-variance model with an L0-norm (cardinality) constraint.
    • Application of the alternating direction method of multipliers (ADMMs) to solve the nonconvex problem.
    • Derivation of the dynamic behavior of the proposed algorithm.

    Main Results:

    • The proposed algorithm allows explicit control over portfolio cardinality.
    • Numerical results show superior performance compared to state-of-the-art algorithms.
    • Demonstrated effectiveness on four real-world datasets.

    Conclusions:

    • The developed ADMM-based algorithm effectively solves the cardinality-constrained nonconvex portfolio optimization problem.
    • This approach offers explicit control over portfolio size, a key advantage over traditional methods.
    • The findings suggest a more precise and controllable method for sparse portfolio construction.