786 citations · 2.1k across the 35 of their papers we have counts for
39 papers
Fast convergence of trust-regions for non-isolated minima via analysis of CG on indefinite matrices
Quentin Rebjock, Nicolas Boumal
Trust-region methods (TR) can converge quadratically to minima where the Hessian is positive definite. However, if the minima are not isolated, then the Hessian there cannot be pos…
Open Problem: Polynomial linearly-convergent method for geodesically convex optimization?
Christopher Criscitiello, David Martínez-Rubio, Nicolas Boumal
Let be a Lipschitz and geodesically convex function defined on a -dimensional Riemannian manifold . Does there exist a first-o…
Benign landscapes of low-dimensional relaxations for orthogonal synchronization on general graphs
Andrew D. McRae, Nicolas Boumal
Orthogonal group synchronization is the problem of estimating elements from the orthogonal group given some relative measurements $R_{ij} \appro…
Fast convergence to non-isolated minima: four equivalent conditions for functions
Quentin Rebjock, Nicolas Boumal
Optimization algorithms can see their local convergence rates deteriorate when the Hessian at the optimum is singular. These singularities are inescapable when the optima are non-i…
The effect of smooth parametrizations on nonconvex optimization landscapes
Eitan Levin, Joe Kileel, Nicolas Boumal
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…
Computing second-order points under equality constraints: revisiting Fletcher's augmented Lagrangian
Florentin Goyens, Armin Eftekhari, Nicolas Boumal
We address the problem of minimizing a smooth function under smooth equality constraints. Under regularity assumptions on these constraints, we propose a notion of approximate firs…