9 citations · 19 across the 10 of their papers we have counts for
10 papers
A geodesic convexity-like structure for the polar decomposition of a square matrix
Foivos Alimisis, Bart Vandereycken
We make a full landscape analysis of the (generally non-convex) orthogonal Procrustes problem. This problem is equivalent to computing the polar factor of a square matrix. We revea…
A preconditioned inverse iteration with an improved convergence guarantee
Foivos Alimisis, Daniel Kressner, Nian Shao +1
Preconditioned eigenvalue solvers offer the possibility to incorporate preconditioners for the solution of large-scale eigenvalue problems, as they arise from the discretization of…
A Nesterov-style Accelerated Gradient Descent Algorithm for the Symmetric Eigenvalue Problem
Foivos Alimisis, Simon Vary, Bart Vandereycken
We develop an accelerated gradient descent algorithm on the Grassmann manifold to compute the subspace spanned by a number of leading eigenvectors of a symmetric positive semi-defi…
Characterization of optimization problems that are solvable iteratively with linear convergence
Foivos Alimisis
In this work, we state a general conjecture on the solvability of optimization problems via algorithms with linear convergence guarantees. We make a first step towards examining it…
Gradient-type subspace iteration methods for the symmetric eigenvalue problem
Foivos Alimisis, Yousef Saad, Bart Vandereycken
This paper explores variants of the subspace iteration algorithm for computing approximate invariant subspaces. The standard subspace iteration approach is revisited and new varian…
Geodesic Convexity of the Symmetric Eigenvalue Problem and Convergence of Riemannian Steepest Descent
Foivos Alimisis, Bart Vandereycken
We study the convergence of the Riemannian steepest descent algorithm on the Grassmann manifold for minimizing the block version of the Rayleigh quotient of a symmetric matrix. Eve…
Distributed Principal Component Analysis with Limited Communication
Foivos Alimisis, Peter Davies, Bart Vandereycken +1
We study efficient distributed algorithms for the fundamental problem of principal component analysis and leading eigenvector computation on the sphere, when the data are randomly…
Communication-Efficient Distributed Optimization with Quantized Preconditioners
Foivos Alimisis, Peter Davies, Dan Alistarh
We investigate fast and communication-efficient algorithms for the classic problem of minimizing a sum of strongly convex and smooth functions that are distributed among differ…
Momentum Improves Optimization on Riemannian Manifolds
Foivos Alimisis, Antonio Orvieto, Gary Bécigneul +1
We develop a new Riemannian descent algorithm that relies on momentum to improve over existing first-order methods for geodesically convex optimization. In contrast, accelerated co…
A Continuous-time Perspective for Modeling Acceleration in Riemannian Optimization
Foivos Alimisis, Antonio Orvieto, Gary Bécigneul +1
We propose a novel second-order ODE as the continuous-time limit of a Riemannian accelerated gradient-based method on a manifold with curvature bounded from below. This ODE can be…