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A Revision on Geodesic Pseudo-Convex Combination and Knaster–Kuratowski–Mazurkiewicz Theorem on Hadamard Manifolds
- Source :
- Journal of Optimization Theory and Applications. 182:1186-1198
- Publication Year :
- 2019
- Publisher :
- Springer Science and Business Media LLC, 2019.
-
Abstract
- In this paper, we point out that a recent characterization of geodesic convex hull on Hadamard manifolds is not rigorous and explain why the characterization does not hold like it in linear spaces. Therefore, a definition of geodesic pseudo-convex combination is proposed to show that the Knaster–Kuratowski–Mazurkiewicz theorem still holds under some mild conditions on Hadamard manifolds.
- Subjects :
- Convex hull
Pure mathematics
021103 operations research
Control and Optimization
Geodesic
Applied Mathematics
0211 other engineering and technologies
Mathematics::General Topology
Hadamard manifold
010103 numerical & computational mathematics
02 engineering and technology
Management Science and Operations Research
Characterization (mathematics)
01 natural sciences
Hadamard transform
Theory of computation
Mathematics::Metric Geometry
Point (geometry)
Convex combination
Mathematics::Differential Geometry
0101 mathematics
Mathematics
Subjects
Details
- ISSN :
- 15732878 and 00223239
- Volume :
- 182
- Database :
- OpenAIRE
- Journal :
- Journal of Optimization Theory and Applications
- Accession number :
- edsair.doi...........9b4ee81341104fcab3399487a5da53b7