Newton's method for B-differentiable equations
Mathematics of Operations Research
A nonsmooth version of Newton's method
Mathematical Programming: Series A and B
Convergence analysis of some algorithms for solving nonsmooth equations
Mathematics of Operations Research
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The aim of this paper is to give an algorithm for solving nondifferentiable equations using the generalized Jacobians with applications in contact problems. In contact problems, the functional which describes the contact conditions and the influence of the frictions is nondifferentiable. A nonsmooth model for solving by damped Newton method the nonsmooth equations, is presented, in which the variables are related to the candidate contact nodes, and which modeling the influence of the friction and the contact conditions. Some definitions, results and algorithms from nonsmooth analysis are presented which leads to some sufficient conditions such that the nonlinear and nondifferentiable system obtained in modeling the contact problems with friction, have one solution obtained by Newton's method using generalized gradient.