216 citations · 1k across the 31 of their papers we have counts for
21 papers · 1 filter
Optimal inexactness schedules for Tunable Oracle based Methods
Guillaume Van Dessel, François Glineur
Several recent works address the impact of inexact oracles in the convergence analysis of modern first-order optimization techniques, e.g. Bregman Proximal Gradient and Prox-Linear…
On the Worst-Case Analysis of Cyclic Coordinate-Wise Algorithms on Smooth Convex Functions
Yassine Kamri, Julien M. Hendrickx, François Glineur
We propose a unifying framework for the automated computer-assisted worst-case analysis of cyclic block coordinate algorithms in the unconstrained smooth convex optimization setup.…
Conic-Optimization Based Algorithms for Nonnegative Matrix Factorization
Valentin Leplat, Yurii Nesterov, Nicolas Gillis +1
Nonnegative matrix factorization is the following problem: given a nonnegative input matrix and a factorization rank , compute two nonnegative matrices, with columns…
New Riemannian preconditioned algorithms for tensor completion via polyadic decomposition
Shuyu Dong, Bin Gao, Yu Guan +1
We propose new Riemannian preconditioned algorithms for low-rank tensor completion via the polyadic decomposition of a tensor. These algorithms exploit a non-Euclidean metric on th…
Extended Formulations for Order Polytopes through Network Flows
Clintin P. Davis-Stober, Jean-Paul Doignon, Samuel Fiorini +2
Mathematical psychology has a long tradition of modeling probabilistic choice via distribution-free random utility models and associated random preference models. For such models,…
Worst-case convergence analysis of inexact gradient and Newton methods through semidefinite programming performance estimation
Etienne de Klerk, Francois Glineur, Adrien Taylor
We provide new tools for worst-case performance analysis of the gradient (or steepest descent) method of Cauchy for smooth strongly convex functions, and Newton's method for self-c…
Algorithms for Positive Semidefinite Factorization
Arnaud Vandaele, François Glineur, Nicolas Gillis
This paper considers the problem of positive semidefinite factorization (PSD factorization), a generalization of exact nonnegative matrix factorization. Given an -by- nonnega…
Exact worst-case convergence rates of the proximal gradient method for composite convex minimization
Adrien B. Taylor, Julien M. Hendrickx, François Glineur
We study the worst-case convergence rates of the proximal gradient method for minimizing the sum of a smooth strongly convex function and a non-smooth convex function whose proxima…
A robust convex optimization framework for autonomous network planning under load uncertainty
Benoît Martin, François Glineur, Emmanuel De Jaeger
Autonomous microgrid planning is a Mixed-Integer Non Convex decision problem that requires to consider investments in both distribution and generation capacity and represents signi…
On the worst-case complexity of the gradient method with exact line search for smooth strongly convex functions
Etienne de Klerk, François Glineur, Adrien B. Taylor
We consider the gradient (or steepest) descent method with exact line search applied to a strongly convex function with Lipschitz continuous gradient. We establish the exact worst-…
Exact Worst-case Performance of First-order Methods for Composite Convex Optimization
Adrien B. Taylor, Julien M. Hendrickx, François Glineur
We provide a framework for computing the exact worst-case performance of any algorithm belonging to a broad class of oracle-based first-order methods for composite convex optimizat…
Complexity of first order inexact Lagrangian and penalty methods for conic convex programming
Ion Necoara, Andrei Patrascu, Francois Glineur
In this paper we present a complete iteration complexity analysis of inexact first order Lagrangian and penalty methods for solving cone constrained convex problems that have or ma…
On the Linear Extension Complexity of Regular n-gons
Arnaud Vandaele, Nicolas Gillis, François Glineur
In this paper, we propose new lower and upper bounds on the linear extension complexity of regular -gons. Our bounds are based on the equivalence between the computation of (i)…
Smooth Strongly Convex Interpolation and Exact Worst-case Performance of First-order Methods
Adrien B. Taylor, Julien M. Hendrickx, François Glineur
We show that the exact worst-case performance of fixed-step first-order methods for unconstrained optimization of smooth (possibly strongly) convex functions can be obtained by sol…
Heuristics for Exact Nonnegative Matrix Factorization
Arnaud Vandaele, Nicolas Gillis, François Glineur +1
The exact nonnegative matrix factorization (exact NMF) problem is the following: given an -by- nonnegative matrix and a factorization rank , find, if possible, an -…
Two Algorithms for Orthogonal Nonnegative Matrix Factorization with Application to Clustering
Filippo Pompili, Nicolas Gillis, P. -A. Absil +1
Approximate matrix factorization techniques with both nonnegativity and orthogonality constraints, referred to as orthogonal nonnegative matrix factorization (ONMF), have been rece…
Accelerated Multiplicative Updates and Hierarchical ALS Algorithms for Nonnegative Matrix Factorization
Nicolas Gillis, François Glineur
Nonnegative matrix factorization (NMF) is a data analysis technique used in a great variety of applications such as text mining, image processing, hyperspectral data analysis, comp…
Low-Rank Matrix Approximation with Weights or Missing Data is NP-hard
Nicolas Gillis, François Glineur
Weighted low-rank approximation (WLRA), a dimensionality reduction technique for data analysis, has been successfully used in several applications, such as in collaborative filteri…
On the Geometric Interpretation of the Nonnegative Rank
Nicolas Gillis, François Glineur
The nonnegative rank of a nonnegative matrix is the minimum number of nonnegative rank-one factors needed to reconstruct it exactly. The problem of determining this rank and comput…
A Multilevel Approach For Nonnegative Matrix Factorization
Nicolas Gillis, François Glineur
Nonnegative Matrix Factorization (NMF) is the problem of approximating a nonnegative matrix with the product of two low-rank nonnegative matrices and has been shown to be particula…
Using Underapproximations for Sparse Nonnegative Matrix Factorization
Nicolas Gillis, François Glineur
Nonnegative Matrix Factorization consists in (approximately) factorizing a nonnegative data matrix by the product of two low-rank nonnegative matrices. It has been successfully app…