Generalized damped Newton algorithms in nonsmooth optimization via second-order subdifferentials

The paper proposes and develops new globally convergent algorithms of the generalized damped Newton type for solving important classes nonsmooth optimization problems. These are based on theory calculations second-order subdifferentials functions with employing machinery variational analysis differentiation. First we develop a superlinearly Newton-type algorithm class continuously differentiable Lipschitzian gradients, which second order. Then design such to solve structured quadratic composite problems extended-real-valued cost functions, typically arise in machine learning statistics. Finally, present results numerical experiments compare performance our main applied an Lasso those achieved by other first-order algorithms.