## The stability of a gradient flow ( discrete scheme, JKO, proximal point, reference request)

Define a free energy functional on the space of probability densities ( on Rd, denoted P(Rn)) E(ρ):=∫Rdf(x)ρ(x)dx+∫Rdρ(x)logρ(x)dx, for some uniformly convex, Lipschitz, non-negative f:Rn→R. Consider the following discrete scheme of a Wasserstein gradient flow ( coined JKO scheme ) : Fix a time step h, given a density with finite second moment ρ0 such that … Read more

## Gradient descent via polynomial approximation

It seems that most proofs of convergence for gradient descent algorithms rely on strong conditions on the first and second derivatives of the function, for instance that |f”(x)| \leq K over the whole domain of the function. My question is are there results for gradient descent type algorithms when we can only say something like … Read more