A concave optimization-based approach for sparse multiobjective programming

  • Guido Cocchi
  • Tommaso Levato
  • Giampaolo LiuzziEmail author
  • Marco Sciandrone
Original Paper


The paper is concerned with multiobjective sparse optimization problems, i.e. the problem of simultaneously optimizing several objective functions and where one of these functions is the number of the non-zero components (or the \(\ell _0\)-norm) of the solution. We propose to deal with the \(\ell _0\)-norm by means of concave approximations depending on a smoothing parameter. We state some equivalence results between the original nonsmooth problem and the smooth approximated problem. We are thus able to define an algorithm aimed to find sparse solutions and based on the steepest descent framework for smooth multiobjective optimization. The numerical results obtained on a classical application in portfolio selection and comparison with existing codes show the effectiveness of the proposed approach.


Multiple objective programming Sparse optimization Concave programming Multiobjective steepest descent methods 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Dipartimento di Ingegneria dell’InformazioneUniversità di FirenzeFlorenceItaly
  2. 2.Istituto di Analisi dei Sistemi ed InformaticaConsiglio Nazionale delle RicercheRomeItaly

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