An Extension of the Kaliszewski Cone to Non-polyhedral Pointed Cones in Infinite-Dimensional Spaces

  • Lidia Huerga
  • Baasansuren Jadamba
  • Miguel SamaEmail author


In this paper, we propose an extension of the family of constructible dilating cones given by Kaliszewski (Quantitative Pareto analysis by cone separation technique, Kluwer Academic Publishers, Boston, 1994) from polyhedral pointed cones in finite-dimensional spaces to a general family of closed, convex, and pointed cones in infinite-dimensional spaces, which in particular covers all separable Banach spaces. We provide an explicit construction of the new family of dilating cones, focusing on sequence spaces and spaces of integrable functions equipped with their natural ordering cones. Finally, using the new dilating cones, we develop a conical regularization scheme for linearly constrained least-squares optimization problems. We present a numerical example to illustrate the efficacy of the proposed framework.


Constrained convex optimization Dilating cones Infinite-dimensional analysis Perturbation theory Proper efficiency 

Mathematics Subject Classification

90C20 90C31 90C46 



Baasansuren Jadamba’s work is supported by RITs COS FEAD Grant for 2016-2017 and the National Science Foundation Grant under Award No. 1720067. Lidia Huerga and Miguel Sama’s work is supported by Ministerio de Economía y Competitividad (Spain) under Project MTM2015-68103-P. The authors are very grateful to the anonymous referees for their useful suggestions and remarks.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Lidia Huerga
    • 1
  • Baasansuren Jadamba
    • 2
  • Miguel Sama
    • 1
    Email author
  1. 1.Departamento de Matemática AplicadaE.T.S.I. Industriales Universidad Nacional de Educación a DistanciaMadridSpain
  2. 2.Center for Applied and Computational Mathematics, School of Mathematical SciencesRochester Institute of TechnologyRochesterUSA

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