Abstract Recently a, monotone generalized directional derixrative has been introduced for Lipschitz functions. This concept has been applied to represent and optimize nonsmooth functions. The second a.pplication resul...Abstract Recently a, monotone generalized directional derixrative has been introduced for Lipschitz functions. This concept has been applied to represent and optimize nonsmooth functions. The second a.pplication result,ed relevant for parallel computing, by allowing to define minimization algorithms with high degree of inherent parallelism. The paper presents first the theoretical 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 steel>est descent direction. Therefore the minimization algorithms are outlined. Successively the used architectures and the performed numerical expertence are described, by listing and commenting the t.ested functions and the obtained results.展开更多
文摘Abstract Recently a, monotone generalized directional derixrative has been introduced for Lipschitz functions. This concept has been applied to represent and optimize nonsmooth functions. The second a.pplication result,ed relevant for parallel computing, by allowing to define minimization algorithms with high degree of inherent parallelism. The paper presents first the theoretical 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 steel>est descent direction. Therefore the minimization algorithms are outlined. Successively the used architectures and the performed numerical expertence are described, by listing and commenting the t.ested functions and the obtained results.
