Hu, T. C.; Klee, Victor; Larman, David Optimization of globally convex functions. (English) Zbl 0686.52006 SIAM J. Control Optimization 27, No. 5, 1026-1047 (1989). 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 Cited in 2 ReviewsCited in 24 Documents MSC: 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) Keywords:quasiconvex; optimization; convex body; Euclidean space; extreme point; max-norm PDFBibTeX XMLCite \textit{T. C. Hu} et al., SIAM J. Control Optim. 27, No. 5, 1026--1047 (1989; Zbl 0686.52006) Full Text: DOI Link