Calvin Wylie

A simple Newton method for local nonsmooth optimization

  • Adrian Lewis
  • Calvin Wylie
    • Categories Nonsmooth Optimization Tags , , , ,

    Superlinear convergence has been an elusive goal for black-box nonsmooth optimization. Even in the convex case, the subgradient method is very slow, and while some cutting plane algorithms, including traditional bundle methods, are popular in practice, local convergence is still sluggish. Faster variants depend either on problem structure or on analyses that elide sequences of … Read more

    Active-set Newton methods and partial smoothness

  • Adrian Lewis
  • Calvin Wylie
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization, Nonsmooth Optimization Tags , ,

    Diverse optimization algorithms correctly identify, in finite time, intrinsic constraints that must be active at optimality. Analogous behavior extends beyond optimization to systems involving partly smooth operators, and in particular to variational inequalities over partly smooth sets. As in classical nonlinear programming, such active-set structure underlies the design of accelerated local algorithms of Newton type. … Read more