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Towards optimization techniques on diffeological spaces
Author(s) -
Goldammer Nico,
Welker Kathrin
Publication year - 2021
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.202000040
Subject(s) - generalization , tangent , mathematics , pure mathematics , tangent space , computer science , natural (archaeology) , algebra over a field , mathematical analysis , geography , geometry , archaeology
Diffeological spaces firstly introduced by J.M. Souriau in the 1980s are a natural generalization of smooth manifolds. In this paper, we give a short overview of the necessary objects for optimization techniques on diffeological spaces. More precisely, we generalize the concepts of tangent spaces, Riemannian structures, retractions and Levi‐Civita connections.