Publications related to Derivatives with respect to metrics and applications: subgradient marching algorithm

The effect of smooth parametrizations on nonconvex optimization landscapes

We develop new tools to study landscapes in nonconvex optimization. Given one optimization problem, we pair it with another by smoothly parametrizing the domain. This is either for practical purposes (e.g., to use smooth optimization algorithms with good g ...

Springer Heidelberg2024

Spatiotemporal energy-density distribution of time-reversed electromagnetic fields

Marcos Rubinstein, Farhad Rachidi-Haeri, Hamidreza Karami, Elias Per Joachim Le Boudec, Nicolas Mora Parra

Time reversal exploits the invariance of electromagnetic wave propagation in reciprocal and lossless media to localise radiating sources. Time-reversed measurements are back-propagated in a simulated domain and converge to the unknown source location. The ...

2023

An Accelerated First-Order Method for Non-convex Optimization on Manifolds

Nicolas Boumal, Christopher Arnold Criscitiello

We describe the first gradient methods on Riemannian manifolds to achieve accelerated rates in the non-convex case. Under Lipschitz assumptions on the Riemannian gradient and Hessian of the cost function, these methods find approximate first-order critical ...

SPRINGER2022

Continuation Methods For Riemannian Optimization

Daniel Kressner, Axel Elie Joseph Séguin

Numerical continuation in the context of optimization can be used to mitigate convergence issues due to a poor initial guess. In this work, we extend this idea to Riemannian optimization problems, that is, the minimization of a target function on a Riemann ...

SIAM PUBLICATIONS2022

Learning to Represent and Reconstruct 3D Deformable Objects

Jan Bednarík

Representing and reconstructing 3D deformable shapes are two tightly linked problems that have long been studied within the computer vision field. Deformable shapes are truly ubiquitous in the real world, whether be it specific object classes such as human ...

EPFL2022

A first-order primal-dual method with adaptivity to local smoothness

Volkan Cevher, Maria-Luiza Vladarean

We consider the problem of finding a saddle point for the convex-concave objective

\min_x \max_y f(x) + \langle Ax, y\rangle - g^*(y)

, where

f

is a convex function with locally Lipschitz gradient and

g

is convex and possibly non-smooth. We propose an ...

2021

Geodesic flows on real forms of complex semi-simple Lie groups of rigid body type

Tudor Ratiu

The geodesic flows are studied on real forms of complex semi-simple Lie groups with respect to a left-invariant (pseudo-)Riemannian metric of rigid body type. The Williamson types of the isolated relative equilibria on generic adjoint orbits are determined ...

SPRINGER INTERNATIONAL PUBLISHING AG2020

Adaptive Gradient Descent without Descent

Konstantin Mishchenko

We present a strikingly simple proof that two rules are sufficient to automate gradient descent: 1) don’t increase the stepsize too fast and 2) don’t overstep the local curvature. No need for functional values, no line search, no information about the func ...

2020

Sampling can be faster than optimization

Nicolas Henri Bernard Flammarion

Optimization algorithms and Monte Carlo sampling algorithms have provided the computational foundations for the rapid growth in applications of statistical machine learning in recent years. There is, however, limited theoretical understanding of the relati ...

PNAS2019

Improving hand and wrist activity detection using tactile sensors and tensor regression methods on Riemannian manifolds

Sylvain Calinon, Noémie Laure Gwendoline Jaquier

Simultaneous and proportional control of a prosthetic hand and wrist is still a controversial issue, although giant steps have lately been made in this direction. In this paper, we study the application of a novel machine learning method to the problem, wi ...

2017

Derivatives with respect to metrics and applications: subgradient marching algorithm

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The effect of smooth parametrizations on nonconvex optimization landscapes

Spatiotemporal energy-density distribution of time-reversed electromagnetic fields

An Accelerated First-Order Method for Non-convex Optimization on Manifolds

Continuation Methods For Riemannian Optimization

Learning to Represent and Reconstruct 3D Deformable Objects

A first-order primal-dual method with adaptivity to local smoothness

Geodesic flows on real forms of complex semi-simple Lie groups of rigid body type

Adaptive Gradient Descent without Descent

Sampling can be faster than optimization

Improving hand and wrist activity detection using tactile sensors and tensor regression methods on Riemannian manifolds

An Accelerated First-Order Method for Non-convex Optimization on Manifolds

The effect of smooth parametrizations on nonconvex optimization landscapes

Spatiotemporal energy-density distribution of time-reversed electromagnetic fields

Continuation Methods For Riemannian Optimization

Learning to Represent and Reconstruct 3D Deformable Objects

A first-order primal-dual method with adaptivity to local smoothness

Adaptive Gradient Descent without Descent

Improving hand and wrist activity detection using tactile sensors and tensor regression methods on Riemannian manifolds

Geodesic flows on real forms of complex semi-simple Lie groups of rigid body type

Sampling can be faster than optimization