Globally convergent coderivative-based generalized Newton methods in nonsmooth optimization

Pham Duy Khanh, Boris Mordukhovich, Vo Thanh Phat, Dat Ba Tran

Abstract: This paper proposes and justifies two globally convergent Newton-type methods to solve unconstrained and constrained problems of nonsmooth optimization by using tools of variational analysis and generalized differentiation. Both methods are coderivative-based and employ generalized Hessians (coderivatives of subgradient mappings) associated with objective functions, which are either of class , or are represented in the form of convex composite optimization, where one of the terms may be extended-real-valued. The proposed globally convergent algorithms are of two types. The first one extends the damped Newton method and requires positive-definiteness of the generalized Hessians for its well-posedness and efficient performance, while the other algorithm is of the regularized Newton-type being well-defined when the generalized Hessians are merely positive-semidefinite. The obtained convergence …