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On the Convergence of Inexact Alternate Minimization in Problems with $$\ell _0$$ ℓ 0 Penalties

Author

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  • Matteo Lapucci

    (Università di Firenze)

  • Alessio Sortino

    (Università di Firenze)

Abstract

In this work, we consider unconstrained nonlinear optimization problems where the objective function presents a penalty term on the cardinality of a subset of the variables vector; specifically, we prove that an alternate minimization scheme has global asymptotic convergence guarantees towards points satisfying first-order optimality conditions, even when the optimization step with respect to one of the blocks of variables is inexact and without introducing proximal terms. This result, supported by numerical evidence, justifies the use of pure alternate minimization in applications, even in absence of convexity assumptions.

Suggested Citation

  • Matteo Lapucci & Alessio Sortino, 2024. "On the Convergence of Inexact Alternate Minimization in Problems with $$\ell _0$$ ℓ 0 Penalties," SN Operations Research Forum, Springer, vol. 5(2), pages 1-11, June.
    • Handle: RePEc:spr:snopef:v:5:y:2024:i:2:d:10.1007_s43069-024-00323-x
    DOI: 10.1007/s43069-024-00323-x
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    References listed on IDEAS

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    1. Nicholas Gould & Dominique Orban & Philippe Toint, 2015. "CUTEst: a Constrained and Unconstrained Testing Environment with safe threads for mathematical optimization," Computational Optimization and Applications, Springer, vol. 60(3), pages 545-557, April.
    2. Christian Kanzow & Matteo Lapucci, 2023. "Inexact penalty decomposition methods for optimization problems with geometric constraints," Computational Optimization and Applications, Springer, vol. 85(3), pages 937-971, July.
    3. Matteo Lapucci & Tommaso Levato & Marco Sciandrone, 2021. "Convergent Inexact Penalty Decomposition Methods for Cardinality-Constrained Problems," Journal of Optimization Theory and Applications, Springer, vol. 188(2), pages 473-496, February.
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