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

Lidia Huerga (), Baasansuren Jadamba () and Miguel Sama ()
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Lidia Huerga: E.T.S.I. Industriales Universidad Nacional de Educación a Distancia
Baasansuren Jadamba: Rochester Institute of Technology
Miguel Sama: E.T.S.I. Industriales Universidad Nacional de Educación a Distancia

Journal of Optimization Theory and Applications, 2019, vol. 181, issue 2, No 4, 437-455

Abstract: Abstract 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.

Keywords: Constrained convex optimization; Dilating cones; Infinite-dimensional analysis; Perturbation theory; Proper efficiency; 90C20; 90C31; 90C46 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10957-018-01468-6

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