Cardinality-Constrained Multi-objective Optimization: Novel Optimality Conditions and Algorithms

Matteo Lapucci () and Pierluigi Mansueto ()
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Matteo Lapucci: University of Florence
Pierluigi Mansueto: University of Florence

Journal of Optimization Theory and Applications, 2024, vol. 201, issue 1, No 13, 323-351

Abstract: Abstract In this paper, we consider multi-objective optimization problems with a sparsity constraint on the vector of variables. For this class of problems, inspired by the homonymous necessary optimality condition for sparse single-objective optimization, we define the concept of L-stationarity and we analyze its relationships with other existing conditions and Pareto optimality concepts. We then propose two novel algorithmic approaches: the first one is an iterative hard thresholding method aiming to find a single L-stationary solution, while the second one is a two-stage algorithm designed to construct an approximation of the whole Pareto front. Both methods are characterized by theoretical properties of convergence to points satisfying necessary conditions for Pareto optimality. Moreover, we report numerical results establishing the practical effectiveness of the proposed methodologies.

Keywords: Multi-objective optimization; Cardinality constraints; Optimality conditions; Numerical methods; Pareto front; 90C26; 90C29; 90C46 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02397-3

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