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Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexity

Nicolas Henri Bernard Flammarion

We consider minimizing a nonconvex, smooth function

f

on a Riemannian manifold

\mathcal{M}

. We show that a perturbed version of Riemannian gradient descent algorithm converges to a second-order stationary point (and hence is able to escape saddle point ...

2019

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Chattez avec Graph Search

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An Inexact Augmented Lagrangian Framework for Nonconvex Optimization with Nonlinear Constraints

Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexity

On the Averaged Green’s Function of an Elliptic Equation with Random Coefficients

Method and system for the creation of an h-spline based data structure, data storage, and data representation

Escaping from saddle points on Riemannian manifolds

Steady Three-Dimensional Rotational Flows: An Approach Via Two Stream Functions And Nash-Moser Iteration

Complex magnetoelectric effect in multiferroic composites: the case of PFN- PT/(Co,Ni)Fe2O4

To positivity and beyond, where Higgs-Dilaton inflation has never gone before

On the choice of metric in gradient-based theories of brain function

Escaping from saddle points on Riemannian manifolds

Optimal Spline Generators for Derivative Sampling

Steady Three-Dimensional Rotational Flows: An Approach Via Two Stream Functions And Nash-Moser Iteration

Complex magnetoelectric effect in multiferroic composites: the case of PFN- PT/(Co,Ni)Fe2O4

On the Averaged Green’s Function of an Elliptic Equation with Random Coefficients

An Inexact Augmented Lagrangian Framework for Nonconvex Optimization with Nonlinear Constraints

Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexity

Method and system for the creation of an h-spline based data structure, data storage, and data representation