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

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, c...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 181; no. 2; pp. 437 - 455
Main Authors: Huerga, Lidia, Jadamba, Baasansuren, Sama, Miguel
Format: Journal Article
Language:English
Published: New York Springer US 01.05.2019
Springer Nature B.V
Subjects:
Applications of Mathematics
Banach spaces
Calculus of Variations and Optimal Control; Optimization
Cones
Engineering
Mathematical functions
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Pareto analysis
Regularization
Theory of Computation
Infinite-dimensional analysis
Perturbation theory
90C20
90C31
90C46
Dilating cones
Constrained convex optimization
Proper efficiency
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary: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.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-018-01468-6