Minimization by Successive Abs-Linearization: Recent Developments
For finite dimensional problems that are unconstrained and piecewise smooth the optimization based on successive abs-linearisation is well analysed yielding for example linear or even quadratic convergence under reasonable assumptions on the function to be optimised. In this talk we discuss the extension of this approach to the more general class of nonsmooth but still Lipschitz continuous functions covering also the Euclidean norm. For this purpose, we introduce the so-called clipped root linearisation and present first numerical results.
Furthermore, we sketch the extansion of this approach to the infinite dimensional setting.