Generalized Newton's Method for $LC^1$ Unconstrained Optimization

Abstract

In this paper the generalized Newton's method for $LC^1$ unconstrained optimization is investigated. This method is an extension of Newton's method for the smooth optimization. Some basic concepts are introduced according to Clarke(1983). We give optimality conditions for this kind of optimization problems. The local and the global convergence with exact line search are established under the condition of semismoothness.