Some Remarks on Cone-Functions and Related Fields

Carla Antoni () and Mohammed Alshahrani ()
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Carla Antoni: Naval Academy
Mohammed Alshahrani: King Fahd University of Petroleum and Minerals

Journal of Optimization Theory and Applications, 2018, vol. 177, issue 3, No 15, 857-864

Abstract: Abstract The classic field of cone-functions is revisited to show their effectiveness for the applications to vector optimization. Then, another extension of the vector convex functions is considered, namely that of geoconvex functions. It shows that, even for this class, it is conceivable to devise a viable numerical calculus. Finally, a short comment is made about the applications to bilevel vector optimization, which will be carried out in two companion papers quoted in references.

Keywords: Cone; Polar cone; Convexity; Geodesic; Cone-functions; Bilevel problems; Image-space analysis; 26B25; 90C25; 90C29 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10957-017-1202-4

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