Globally Convergent Inexact Generalized Newton Methods With Decreasing Norm Of The Gradient
Ding Guo Pu 11 Department of Mathematics, Tongji University, Shanghai 200331, China
In this paper, motivated by the Martinez and Qi methods[l], we propose one type of globally convergent inexact generalized Newton methods to solve unconstrained optimization problems in which the objective functions are not twice differentiable,but have LC gradient. They make the norm of the gradient decreasing.These methods are implementable and globally convergent. We prove that the algorithms have superlinear convergence rates under some mile conditions.\par The methods may also be used to solve nonsmooth epuations.
Key words: Nonsmooth optimization; Inexact Newton method; Generalized Newton method; Global convergence; Superoinear rate.