nonsmooth optimization

Smoothing Method of Multipliers for Sum-Max Problems

  • Michael Zibulevsky
    • Categories Convex Optimization, Nonsmooth Optimization, Unconstrained Optimization Tags , , ,

    We study nonsmooth unconstrained optimization problem, which includes sum of pairwise maxima of smooth functions. Minimum $l_1$-norm approximation is a particular case of this problem. Combining ideas Lagrange multipliers with smooth approximation of max-type function, we obtain a new kind of nonquadratic augmented Lagrangian. Our approach does not require artificial variables, and preserves sparse structure … Read more

    A bundle filter method for nonsmooth nonlinear optimization

  • Roger Fletcher
  • Sven Leyffer
    • Categories Convex and Nonsmooth Optimization, Nonsmooth Optimization Tags , ,

    We consider minimizing a nonsmooth objective subject to nonsmooth constraints. The nonsmooth functions are approximated by a bundle of subgradients. The novel idea of a filter is used to promote global convergence. Citation NA\195, Department of Mathematics, University of Dundee, UK, December, 1999 Article Download View A bundle filter method for nonsmooth nonlinear optimization