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    Area of Science:

    • Optimization Theory
    • Machine Learning
    • Applied Mathematics

    Background:

    • Nonconvex optimization problems with multiple variables are challenging due to the risk of converging to local minima.
    • Traditional alternating minimization (AM) strategies can be trapped in spurious local minima.
    • Learning-based methods like deep unfolding lack data and explainability for nonconvex optimization.

    Purpose of the Study:

    • To propose a novel meta-learning based alternating minimization (MLAM) method for nonconvex optimization.
    • To address limitations of AM and learning-based approaches in nonconvex settings.
    • To enhance performance and maintain interpretability in optimization algorithms.

    Main Methods:

    • Developed a meta-learning based alternating minimization (MLAM) approach.
    • MLAM minimizes global losses over iterations, learning adaptive strategies.
    • Evaluated MLAM on matrix completion and Gaussian mixture models.

    Main Results:

    • The proposed MLAM method demonstrates superior performance compared to traditional AM-based methods.
    • Experimental results validate the effectiveness of MLAM on representative nonconvex problems.
    • MLAM provides a balance between performance and algorithmic interpretability.

    Conclusions:

    • MLAM offers a promising alternative for solving nonconvex optimization problems.
    • The adaptive learning strategy in MLAM overcomes limitations of fixed updating rules in AM.
    • This approach advances the field of nonconvex optimization with improved efficiency and explainability.