An algorithm based on a combination of the polyhedral and quadratic approximation is given for nding stationary points for unconstrained minimization problems with locally Lipschitz problem functions that are not necessarily convex or di erentiable. Global convergence of the algorithm is established. Under additional assumptions, it is shown that the algorithm generates Newton iterations and that the convergence is superlinear. Some encouraging numerical experience is reported.
Abstract. The main purpose of this paper is to prove g l o b a l c o n vergence of the new trust region method based on smoothed CGS algorithm. This method is suprisingly convenient f o r n umerical solution of large sparse systems of nonlinear equations as it is demonstrated by n umerical experiments. A modi cation of the proposed trust region method do not use matrices, so it can be used for large dense systems of nonlinear equations.
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