Fenchel Problem of Level Sets

T. Rapcsák
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T. Rapcsák: Hungarian Academy of Sciences

Journal of Optimization Theory and Applications, 2005, vol. 127, issue 1, No 10, 177-191

Abstract: Abstract The Fenchel problem of level sets in the smooth case is solved by deducing a new and nice geometric necessary and sufficient condition for the existence of a smooth convex function with the level sets of a given smooth pseudoconvex function. The main theorem is based on a general differential geometric tool, the space of paths defined on smooth manifolds. This approach provides a complete geometric characterization of a new subclass of pseudoconvex functions originating from analytical mechanics and a new view on convexlike and generalized convexlike mappings in image analysis.

Keywords: Fenchel problem of level sets; convex image transformable functions; pseudoconvexity; space of paths (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/s10957-005-6399-y

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