Parallel minimization algorithms by generalized subdifferentiability

Recently a monotone generalized directional derivative has been introduced for Lipschitz functions. This concept has been applied to represent and optimize nonsmooth functions. The second application resulted relevant for parallel computing, by allowing to define minimization algorithms with high degree of inherent parallelism. The paper presents first the teoretical background, namely the notions of monotone generalized directional derivative and monotone generalized subdifferential. Then it defines the tools for the procedures, that is a necessary optimality condition and a steepest descent direction. Therefore the minimization algorithms are outlined. Successively the used architectures and the performed numerical experience are described, by listing and commenting the tested functions and the obtained results.