Bartolomeo Stellato

Exterior-point Optimization for Nonconvex Learning

  • Shuvomoy Das Gupta
  • Bartolomeo Stellato
  • Bart Paul Gerard Van Parys
    • Categories Constrained Nonlinear Optimization, Nonsmooth Optimization, Statistics Tags , , ,

    In this paper we present the nonconvex exterior-point optimization solver (NExOS)—a novel first-order algorithm tailored to constrained nonconvex learning problems. We consider the problem of minimizing a convex function over nonconvex constraints, where the projection onto the constraint set is single-valued around local minima. A wide range of nonconvex learning problems have this structure including … Read more

    Infeasibility detection in the alternating direction method of multipliers for convex optimization

  • Goran Banjac
  • Stephen Boyd
  • Paul J. Goulart
  • Bartolomeo Stellato
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming Tags , , ,

    The alternating direction method of multipliers is a powerful operator splitting technique for solving structured optimization problems. For convex optimization problems, it is well-known that the algorithm generates iterates that converge to a solution, provided that it exists. If a solution does not exist, then the iterates diverge. Nevertheless, we show that they yield conclusive … Read more