Optimization of globally convex functions. (English) Zbl 0686.52006

Globally convex functions are functions that behave “convexly” on triples of widely dispersed, collinear points. In connection with the maximization of globally convex functions over convex bodies in a given finite-dimensional normed space E, for points c of bodies C in E, the maximum is estimated of the ratio between two measures of how close c comes to being an extreme point of C. Good estimates are obtained for the cases in which E is euclidean or has the max-norm.
Reviewer: G.Sierksma


52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
52A40 Inequalities and extremum problems involving convexity in convex geometry
90C25 Convex programming
46B20 Geometry and structure of normed linear spaces
46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)
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