Back to Search
Start Over
BASIC CONVEX ANALYSIS IN METRIC SPACES WITH BOUNDED CURVATURE.
- Source :
- SIAM Journal on Optimization; 2024, Vol. 34 Issue 1, p366-388, 23p
- Publication Year :
- 2024
-
Abstract
- Differentiable structure ensures that many of the basics of classical convex analysis extend naturally from Euclidean space to Riemannian manifolds. Without such structure, however, extensions are more challenging. Nonetheless, in Alexandrov spaces with curvature bounded above (but possibly positive), we develop several basic building blocks. We define subgradients via projection and the normal cone, prove their existence, and relate them to the classical affine minorant property. Then, in what amounts to a simple calculus or duality result, we develop a necessary optimality condition for minimizing the sum of two convex functions. [ABSTRACT FROM AUTHOR]
- Subjects :
- CURVATURE
CONVEX functions
CALCULUS
Subjects
Details
- Language :
- English
- ISSN :
- 10526234
- Volume :
- 34
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- SIAM Journal on Optimization
- Publication Type :
- Academic Journal
- Accession number :
- 176824667
- Full Text :
- https://doi.org/10.1137/23M1551389