...wing nonmonotone choices. The nonmonotone strategies (see for example [10]) are well known in the literature for their effectiveness in the choice of the steplength in many line–search algorithms. In =-=[1]-=- the nonmonotone convergence has been proved in the smooth case for an inexact Newton line–search algorithm and the numerical experience 3shows that the nonmonotone strategies can be useful in this ki...

...ipschitz function near a given point x (with x ∈ ΩF ). The B-subdifferential of F at x is ∂BF (x) = {Z ∈ Rn×n : ∃{xk} * ΩF ,with lim xk→x ∇F (xk)T = Z}. Definition 2.2 (Clarke’s generalized Jacobian (=-=[3]-=-)) Let F : Rn → Rn be a locally Lipschitz function near a given point x. Clarke’s generalized Jacobian of F at x is ∂F (x) = co∂BF (x) where co denotes the convex combinations in the space Rn×n. Remar...