【摘 要】
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Notion of metrically regular property and certain types of point-based approximations are used for solving the nonsmooth generalized equation f(x)+(F)(x)? 0,where X and Y are Banach spaces,and U is an open subset of X,f:U → Y is a nonsmooth function and(F
【机 构】
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Institute of Computational Mathematics and Scientific/Engineering Computing,Academy of Mathematics a
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Notion of metrically regular property and certain types of point-based approximations are used for solving the nonsmooth generalized equation f(x)+(F)(x)? 0,where X and Y are Banach spaces,and U is an open subset of X,f:U → Y is a nonsmooth function and(F):X(→→)Y is a set-valued mapping with closed graph.We introduce a confined Newton-type method for solving the above nonsmooth generalized equation and analyze the semilocal and local convergence of this method.Specifically,under the point-based approximation of f on U and metrically regular property of f+(F),we present quadratic rate of convergence of this method.Furthermore,superlinear rate of convergence of this method is provided under the conditions that f admits p-point-based approximation on U and f+(F)is metrically regular.An example of nonsmooth functions that have p-point-based approximation is given.Moreover,a numerical experiment is given which illustrates the theoretical result,.
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