Alberto Bemporad

Self-concordant smoothing in proximal quasi-Newton algorithms for large-scale convex composite optimization

  • Adeyemi D. Adeoye
  • Alberto Bemporad
    • Categories Convex Optimization, Nonsmooth Optimization Tags , , , , , , ,

    We introduce a notion of self-concordant smoothing for minimizing the sum of two convex functions, one of which is smooth and the other nonsmooth. The key highlight is a natural property of the resulting problem’s structure that yields a variable metric selection method and a step length rule especially suited to proximal quasi-Newton algorithms. Also, … Read more

    Forward-backward truncated Newton methods for convex composite optimization

  • Alberto Bemporad
  • Lorenzo Stella
  • Panagiotis Patrinos
    • Categories Convex Optimization, Nonsmooth Optimization Tags , , , , ,

    This paper proposes two proximal Newton-CG methods for convex nonsmooth optimization problems in composite form. The algorithms are based on a a reformulation of the original nonsmooth problem as the unconstrained minimization of a continuously differentiable function, namely the forward-backward envelope (FBE). The first algorithm is based on a standard line search strategy, whereas the … Read more