composite functions

Minimization of nonsmooth nonconvex functions using inexact evaluations and its worst-case complexity

  • Serge Gratton
  • Philippe L. Toint
  • Ehouarn Simon
    • Categories Constrained Nonlinear Optimization, Nonsmooth Optimization, Unconstrained Optimization Tags , , , ,

    An adaptive regularization algorithm using inexact function and derivatives evaluations is proposed for the solution of composite nonsmooth nonconvex optimization. It is shown that this algorithm needs at most O(|log(epsilon)|.epsilon^{-2}) evaluations of the problem’s functions and their derivatives for finding an $\epsilon$-approximate first-order stationary point. This complexity bound therefore generalizes that provided by [Bellavia, Gurioli, … Read more

    Trust-region methods without using derivatives: Worst case complexity and the non-smooth case

  • R. Garmanjani
  • Luis Nunes Vicente
  • Diogo Júdice
    • Categories Nonsmooth Optimization, Unconstrained Optimization Tags , , , , ,

    Trust-region methods are a broad class of methods for continuous optimization that found application in a variety of problems and contexts. In particular, they have been studied and applied for problems without using derivatives. The analysis of trust-region derivative-free methods has focused on global convergence, and they have been proved to generate a sequence of … Read more

    Composite Proximal Bundle Method

  • Claudia Sagastizábal
    • Categories Convex and Nonsmooth Optimization, Nonsmooth Optimization Tags , ,

    We consider minimization of nonsmooth functions which can be represented as the composition of a positively homogeneous convex function and a smooth mapping. This is a sufficiently rich class that includes max-functions, largest eigenvalue functions, and norm-1 regularized functions. The bundle method uses an oracle that is able to compute separately the function and subgradient … Read more