7 papers · 1 filter
The sketched landing method for large-scale optimization under orthogonality constraints
Florentin Goyens, Simon Mataigne, Pierre-Antoine Absil
We propose the sketched landing method, a randomized variant of the landing method for optimization under orthogonality constraints. Each landing step consists of the sum of a norm…
The Riemannian Landing Method: From projected gradient flows to SQP
Florentin Goyens, Florian Feppon
Landing methods have recently emerged in Riemannian matrix optimization as efficient schemes for handling nonlinear equality constraints without resorting to costly retractions. Th…
Complexity of quadratic penalty methods with adaptive accuracy under a PL condition for the constraints
Florentin Goyens, Geovani N. Grapiglia
We study the quadratic penalty method (QPM) for smooth nonconvex optimization problems with equality constraints. Assuming the constraint violation satisfies the PL condition near…
Complexity guarantees and polling strategies for Riemannian direct-search methods
Bastien Cavarretta, Florentin Goyens, Clément W. Royer +1
Direct-search algorithms are derivative-free optimization techniques that operate by polling the variable space along specific directions forming positive spanning sets (PSSs). Whe…
Riemannian trust-region methods for strict saddle functions with complexity guarantees
Florentin Goyens, Clément W. Royer
The difficulty of minimizing a nonconvex function is in part explained by the presence of saddle points. This slows down optimization algorithms and impacts worst-case complexity g…
Registration of algebraic varieties using Riemannian optimization
Florentin Goyens, Coralia Cartis, Stéphane Chrétien
We consider the point cloud registration problem, the task of finding a transformation between two point clouds that represent the same object but are expressed in different coordi…
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…