Franz Bethke

How Stringent is the Linear Independence Kink Qualification in Abs-Smooth Optimization?

  • Franz Bethke
  • Andrea Walther
    • Categories Nonsmooth Optimization Tags

    Abs-smooth functions are given by compositions of smooth functions and the evaluation of the absolute value. The linear independence kink qualification (LIKQ) is a fundamental assumption in optimization problems governed by these abs-smooth functions, generalizing the well-known LICQ from smooth optimization. In particular, provided that LIKQ holds it is possible to derive optimality conditions for … Read more

    A Semismooth Conjugate Gradients Method — Theoretical Analysis

  • Franz Bethke
  • Andreas Griewank
  • Andrea Walther
    • Categories Nonsmooth Optimization Tags , , ,

    In large scale applications, deterministic and stochastic variants of Cauchy’s steepest descent method are widely used for the minimization of objectives that are only piecewise smooth. In this paper we analyse a  deterministic descent method based on the generalization of rescaled conjugate gradients proposed by Philip Wolfe in 1975 for objectives that are convex. Without … Read more