Sébastien Kerleau

A characterization of positive spanning sets with ties to strongly edge-connected digraphs

  • Denis Cornaz
  • Sébastien Kerleau
  • Clément W. Royer
    • Categories Graphs and Matroids, Nonlinear Optimization, Unconstrained Optimization

    Positive spanning sets (PSSs) are families of vectors that span a given linear space through non-negative linear combinations. Despite certain classes of PSSs being well understood, a complete characterization of PSSs remains elusive. In this paper, we explore a relatively understudied relationship between positive spanning sets and strongly edge-connected digraphs, in that the former can … Read more

    Using orthogonally structured positive bases for constructing positive k-spanning sets with cosine measure guarantees

  • Warren Hare
  • Clément W. Royer
  • Gabriel Jarry-Bolduc
  • Sébastien Kerleau
    • Categories Nonlinear Optimization, Unconstrained Optimization Tags , , , , ,

    Positive spanning sets span a given vector space by nonnegative linear combinations of their elements. These have attracted significant attention in recent years, owing to their extensive use in derivative-free optimization. In this setting, the quality of a positive spanning set is assessed through its cosine measure, a geometric quantity that expresses how well such … Read more