A Unifying Framework for Sparsity-Constrained Optimization

Matteo Lapucci (), Tommaso Levato, Francesco Rinaldi and Marco Sciandrone
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Matteo Lapucci: Università di Firenze
Tommaso Levato: Università di Firenze
Francesco Rinaldi: Università di Padova
Marco Sciandrone: Sapienza Università di Roma

Journal of Optimization Theory and Applications, 2023, vol. 199, issue 2, No 9, 663-692

Abstract: Abstract In this paper, we consider the optimization problem of minimizing a continuously differentiable function subject to both convex constraints and sparsity constraints. By exploiting a mixed-integer reformulation from the literature, we define a necessary optimality condition based on a tailored neighborhood that allows to take into account potential changes of the support set. We then propose an algorithmic framework to tackle the considered class of problems and prove its convergence to points satisfying the newly introduced concept of stationarity. We further show that, by suitably choosing the neighborhood, other well-known optimality conditions from the literature can be recovered at the limit points of the sequence produced by the algorithm. Finally, we analyze the computational impact of the neighborhood size within our framework and in the comparison with some state-of-the-art algorithms, namely, the Penalty Decomposition method and the Greedy Sparse-Simplex method. The algorithms have been tested using a benchmark related to sparse logistic regression problems.

Keywords: Sparsity-constrained problems; Optimality conditions; Stationarity; Numerical methods; Asymptotic convergence; Sparse logistic regression; 90C30; 90C46; 65K05 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02306-0

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