Software
Tensor-based algorithms
Tensorlab+: A reproducible research repository for tensor computations, built on top of Tensorlab.
Structured optimization algorithms
PEPit: Computer-assisted worst-case analyses of first-order optimization methods in Python (Paper).
QPALM: A proximal augmented Lagrangian method for (possibly nonconvex) QPs using semismooth Newton direction and exact line search (Paper).
StructuredOptimization.jl: A high-level modeling language that utilizes a syntax that is very close to the mathematical formulation of an optimization problem.
ProximalOperators.jl: Proximal operators for nonsmooth optimization in Julia.
ProximalAlgorithms.jl: Proximal algorithms (also known as “splitting” algorithms or methods) for nonsmooth optimization in Julia.
AbstractOperators.jl: Abstract operators extend the syntax typically used for matrices to linear mappings of arbitrary dimensions and nonlinear functions. Unlike matrices however, abstract operators apply the mappings with specific efficient algorithms that minimize memory requirements. This is particularly useful in iterative algorithms and in first order large-scale optimization algorithms.
Low-rank optimization algorithms
Quadproj: A Python library to project a point onto a quadratic surface.
A Riemannian Rank-Adaptive Method for low-rank matrix completion. Paper and code.
Riemannian Preconditioned Algorithms for Tensor Completion via Polyadic Decomposition. Paper and code.
Riemannian gradient descent methods for graph-regularized matrix completion. Paper and code.
Data fitting on manifolds with composite Bézier-like curves and blended cubic splines. Paper and code.
Riemannian optimization on the symplectic Stiefel manifold. Paper and code.
Low-rank multi-parametric covariance identification. Paper and code.
Minimum enclosing ball of a collection of linear subspaces. Paper and code.
Computing the matrix geometric mean: Riemannian vs Euclidean conditioning, implementation techniques, and a Riemannian BFGS method. Paper and code.
Riemannian gradient descent methods for graph-regularized matrix completion. Paper and code.
Variable projection applied to block term decomposition of higher-order tensors. Paper and code.
NormalForms: Julia software for solving systems of polynomial equations via normal form methods.
Nonnegative Matrix Factorization
Nonnegative Matrix Factorization. Book and code.
Collection at website Nicolas Gillis.
F-HALS: functional HALS (Hierarchical Alternating Least Squares Algorithm) for Nonnegative Matrix Factorization over Continuous Signals using Parametrizable Functions. Paper.
Data-driven modeling and signal processing
SLRA: Software for weighted structured low-rank approximation. The slra package includes a wrapper function ident for identification of linear time-invariant systems.
A missing data approach to data-driven filtering and control.
Identifiability in the behavioral setting.
Subspace identification with constraints on the impulse response