Geodesic
Newton methods for solving two classes of nonsmooth equations
Applications of Mathematics, Tome 46 (2001) no. 3, pp. 215-229 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The paper is devoted to two systems of nonsmooth equations. One is the system of equations of max-type functions and the other is the system of equations of smooth compositions of max-type functions. The Newton and approximate Newton methods for these two systems are proposed. The Q-superlinear convergence of the Newton methods and the Q-linear convergence of the approximate Newton methods are established. The present methods can be more easily implemented than the previous ones, since they do not require an element of Clarke generalized Jacobian, of B-differential, or of b-differential, at each iteration point.
The paper is devoted to two systems of nonsmooth equations. One is the system of equations of max-type functions and the other is the system of equations of smooth compositions of max-type functions. The Newton and approximate Newton methods for these two systems are proposed. The Q-superlinear convergence of the Newton methods and the Q-linear convergence of the approximate Newton methods are established. The present methods can be more easily implemented than the previous ones, since they do not require an element of Clarke generalized Jacobian, of B-differential, or of b-differential, at each iteration point.
DOI : 10.1023/A:1013791923957
Classification : 65H10, 90C30
Keywords: nonsmooth equations; Newton method; approximate Newton method; max-type function; composite function; convergence 
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Gao, Yan. Newton methods for solving two classes of nonsmooth equations. Applications of Mathematics, Tome 46 (2001) no. 3, pp. 215-229. doi: 10.1023/A:1013791923957

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