Projections onto convex sets on the sphere

In this paper some concepts of convex analysis are extended in an intrinsic way from the Euclidean space to the sphere. In particular, relations between convex sets in the sphere and pointed convex cones are presented. Several characterizations of the usual projection onto a Euclidean convex set are...

Full description

Saved in:
Bibliographic Details
Published inJournal of global optimization Vol. 57; no. 3; pp. 663 - 676
Main Authors Ferreira, O. P., Iusem, A. N., Németh, S. Z.
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.11.2013
Springer
Springer Nature B.V
Subjects
Computer Science
Cones
Convex analysis
Euclidean space
Geometry
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Projection
Real Functions
Studies
Theorems
Sphere
Convex set in the sphere
Pointed convex cone
Projection onto a pointed convex cone
Online AccessGet full text

Cover

More Information
Summary:In this paper some concepts of convex analysis are extended in an intrinsic way from the Euclidean space to the sphere. In particular, relations between convex sets in the sphere and pointed convex cones are presented. Several characterizations of the usual projection onto a Euclidean convex set are extended to the sphere and an extension of Moreau’s theorem for projection onto a pointed convex cone is exhibited.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-012-9914-3