A Unifying Framework for Sparsity-Constrained Optimization

• Published in: Journal of optimization theory and applications Vol. 199; no. 2; pp. 663 - 692
• Main Authors: Lapucci, Matteo, Levato, Tommaso, Rinaldi, Francesco, Sciandrone, Marco
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.11.2023; Springer Nature B.V
• Subjects: Algorithms; Applications of Mathematics; Calculus of Variations and Optimal Control; Optimization; Constraints; Engineering; Greedy algorithms; Impact analysis; Mathematics; Mathematics and Statistics; Mixed integer; Neighborhoods; Operations Research/Decision Theory; Optimization; Penalty function; Sparsity; Theory of Computation; Sparsity-constrained problems; Optimality conditions; 90C30; 65K05; 90C46; Numerical methods; Stationarity; Sparse logistic regression; Asymptotic convergence

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 neighb...