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https://hdl.handle.net/20.500.14365/2110
Title: | A Nonlinear Cone Separation Theorem and Scalarization in Nonconvex Vector Optimization | Authors: | Kasimbeyli̇, Refail | Keywords: | cone separation theorem cone approximation augmented dual cones Bishop-Phelps cones sublinear functions nonconvex vector optimization conic scalarization multiobjective optimization Proper Efficiency Respect Assignment Spaces Set |
Publisher: | Siam Publications | Abstract: | In this paper, a special separation property for two closed cones in Banach spaces is proposed, and a nonlinear separation theorem for the cones possessing this property is proved. By extending a usual definition of dual cones, an augmented dual of a cone is introduced. A special class of monotonically increasing sublinear functions is defined by using the elements of the augmented dual cone. Any closed cone possessing the separation property with its epsilon-conic neighborhood is shown to be approximated arbitrarily closely by a zero sublevel set of some function from this class. As an application, a simple and efficient scalarization technique for nonconvex vector optimization problems is suggested, and it is shown that any properly minimal point of a set in a Banach space can be calculated by minimizing a certain sublinear functional. | URI: | https://doi.org/10.1137/070694089 https://hdl.handle.net/20.500.14365/2110 |
ISSN: | 1052-6234 |
Appears in Collections: | WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection |
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