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Title: 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, 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.  more » « less
Award ID(s):
1720067
PAR ID:
10096178
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Journal of optimization theory and applications
Volume:
181
Issue:
2
ISSN:
0022-3239
Page Range / eLocation ID:
437 - 455
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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