SELF-CONTRACTED CURVES ARE GRADIENT FLOWS OF CONVEX FUNCTIONS

Estibalitz Durand-Cartagena (1) , Antoine Lemenant (2)

1 Departamento de Matemática Aplicada
2 LJLL - Laboratoire Jacques-Louis Lions

In this paper we prove that any C 1,α curve in R n , with α ∈ (1 2 , 1], is the solution of the gradient flow equation for some C 1 convex function f , if and only if it is strongly self-contracted.

Domaines: Mathématiques générales [math.GM]

Estibalitz Durand-Cartagena, Antoine Lemenant. SELF-CONTRACTED CURVES ARE GRADIENT FLOWS OF CONVEX FUNCTIONS. 2018. ⟨hal-01714156⟩