On steepest descent curves for quasi convex families in Rn

DOI10.1002/mana.201300133zbMath1318.52004arXiv1303.3721OpenAlexW2591625315MaRDI QIDQ4982608

Adriana Venturi, Marco Longinetti, Paolo Manselli

Publication date: 9 April 2015

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.3721

zbMATH Keywords

convex bodymean widthsteepest descent curvequasi convex functionsconvex stratificationexpanding coupleself expanding curve

Mathematics Subject Classification ID

Set-valued and variational analysis (49J53) Convex functions and convex programs in convex geometry (52A41) Convex sets in (2) dimensions (including convex curves) (52A10) Convexity of real functions of several variables, generalizations (26B25) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (11)

Rectifiability property for plane paths and descent curves ⋮ Sweeping by a tame process ⋮ Self-contracted curves in Riemannian manifolds ⋮ The slope robustly determines convex functions ⋮ Ubiquitous algorithms in convex optimization generate self-contracted sequences ⋮ Plane R-curves II ⋮ Bounding regions to plane steepest descent curves of quasiconvex families ⋮ Plane R-curves and their steepest descent properties I ⋮ Self-contracted curves in CAT(0)-spaces and their rectifiability ⋮ Metric and geometric relaxations of self-contracted curves ⋮ Rectifiability of self-contracted curves in the Euclidean space and applications

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• Evolution equations with lack of convexity
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• On variational problems related to steepest descent curves and self-dual convex sets on the sphere

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