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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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
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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.
AbstractList	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. 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.
Author	Huerga, Lidia Jadamba, Baasansuren Sama, Miguel
Author_xml	– sequence: 1 givenname: Lidia surname: Huerga fullname: Huerga, Lidia organization: Departamento de Matemática Aplicada, E.T.S.I. Industriales Universidad Nacional de Educación a Distancia – sequence: 2 givenname: Baasansuren surname: Jadamba fullname: Jadamba, Baasansuren organization: Center for Applied and Computational Mathematics, School of Mathematical Sciences, Rochester Institute of Technology – sequence: 3 givenname: Miguel surname: Sama fullname: Sama, Miguel email: msama@ind.uned.es organization: Departamento de Matemática Aplicada, E.T.S.I. Industriales Universidad Nacional de Educación a Distancia
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Cites_doi	10.1016/j.sysconle.2012.03.003 10.1016/0022-247X(79)90226-9 10.1023/B:SVAN.0000023393.75251.05 10.1007/s10589-005-3056-1 10.1007/BF00934357 10.1016/0022-247X(68)90201-1 10.1111/itor.12398 10.1007/s10589-016-9885-2 10.1090/pspum/007/0154092 10.3934/nhm.2014.9.501 10.1007/BF00934353 10.1016/j.na.2009.10.036 10.1016/j.ejor.2015.04.026 10.1080/02331938908843501 10.1016/j.jat.2011.11.001 10.1137/140974584 10.1137/070692789 10.1007/978-1-4615-2772-5 10.1007/BF00935175 10.1090/S0002-9947-1993-1098432-5 10.1137/0315004 10.1080/01630563.2013.806546 10.1525/9780520411586-036 10.1007/978-3-642-57014-8_9
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Copyright	Springer Science+Business Media, LLC, part of Springer Nature 2019 Journal of Optimization Theory and Applications is a copyright of Springer, (2019). All Rights Reserved.
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Snippet	In this paper, we propose an extension of the family of constructible dilating cones given by Kaliszewski (Quantitative Pareto analysis by cone separation...
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SubjectTerms	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
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Title	An Extension of the Kaliszewski Cone to Non-polyhedral Pointed Cones in Infinite-Dimensional Spaces
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