A penalty decomposition approach for multi-objective cardinality-constrained optimization problems. (2nd November 2022)

• Record Type: Journal Article
• Authors: Lapucci, Matteo
• Is Part Of: Optimization methods and software. Volume 37:Number 6(2022)
• Page Start: 2157
• Page End: 2189
• Publication Date: 2022-11-02
• Subjects: Multi-objective optimization -- cardinality constraints -- penalty decomposition method -- global convergence -- portfolio selection problem; 90C26 -- 90C29 -- 90C30; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2022.2060972
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : In this manuscript, we consider multi-objective optimization problems with a cardinality constraint on the vector of decision variables and additional linear constraints. For this class of problems, we analyse necessary and sufficient conditions of Pareto optimality. We afterwards propose a Penalty Decomposition type algorithm, exploiting multi-objective descent methods, to tackle the aforementioned family of problems. We conduct a rigorous convergence analysis for the proposed method, where we prove that the produced sequence of points has limit points, each one being feasible and satisfying first-order optimality conditions. Numerical computational experiments, carried out on instances of relevant real-world problems such as sparse mean/variance portfolio selection and sparse regularized logistic regression, in their multi-objective formulation, show that the proposed procedure is effective at finding solutions forming good Pareto sets approximations.