Achieving linear or quadratic convergence on piecewise smooth optimization problems

Andreas Griewank, Andrea Walther

Abstract:

Many problems in machine learning involve objective functions that
are piecewise smooth due to the occurrence of absolute values mins and maxes in
their evaluation procedures. For such function we derived first
order (KKT) and second order (SSC) optimality conditions, which can be checked on
the basis of a local piecewise linearization that can be computed in an AD like
fashion, e.g. using ADOL-C or Tapenade.