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Nested Alternating Minimization with FISTA for Non-convex and Non-smooth Optimization Problems

Author

Listed:
  • Eyal Gur

    (Technion – Israel Institute of Technology)

  • Shoham Sabach

    (Technion – Israel Institute of Technology)

  • Shimrit Shtern

    (Technion – Israel Institute of Technology)

Abstract

Motivated by a recent framework for proving global convergence to critical points of nested alternating minimization algorithms, which was proposed for the case of smooth subproblems, we first show here that non-smooth subproblems can also be handled within this framework. Specifically, we present a novel analysis of an optimization scheme that utilizes the FISTA method as a nested algorithm. We establish the global convergence of this nested scheme to critical points of non-convex and non-smooth optimization problems. In addition, we propose a hybrid framework that allows to implement FISTA when applicable, while still maintaining the global convergence result. The power of nested algorithms using FISTA in the non-convex and non-smooth setting is illustrated with some numerical experiments that show their superiority over existing methods.

Suggested Citation

  • Eyal Gur & Shoham Sabach & Shimrit Shtern, 2023. "Nested Alternating Minimization with FISTA for Non-convex and Non-smooth Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 199(3), pages 1130-1157, December.
    • Handle: RePEc:spr:joptap:v:199:y:2023:i:3:d:10.1007_s10957-023-02310-4
    DOI: 10.1007/s10957-023-02310-4
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