A. Vandaele

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math.OC2026

Computing Lower Bounds on the Nonnegative Rank via Non-Convex Optimization Solvers

Timothy Baeckelant, Arnaud Vandaele, Nicolas Gillis

The nonnegative rank of a nonnegative matrix $X$ is the smallest number of nonnegative rank-one factors that sum to $X$ . Since computing the nonnegative rank is NP-hard, it is comm…

math.OC2026

Manifold-based Algorithms for the Hadamard Decomposition

Nicolas Gillis, Subhayan Saha, Stefano Sicilia +1

Given a matrix $X$ , and two ranks $r_{1}$ and $r_{2}$ , the Hadamard decomposition (HD) looks for two low-rank matrices, $X_{1}$ of rank $r_{1}$ and $X_{2}$ of rank $r_{2}$ , both of the same si…