Newton and Quasi-Newton Methods for a Class of Nonsmooth Equations and Related Problems

نویسندگان

Defeng Sun

Jiye Han

چکیده

The paper presents concrete realizations of quasi-Newton methods for solving several standard problems including complementarity problems, special variational inequality problems, and the Karush–Kuhn–Tucker (KKT) system of nonlinear programming. A new approximation idea is introduced in this paper. The Q-superlinear convergence of the Newton method and the quasiNewton method are established under suitable assumptions, in which the existence of F ′(x∗) is not assumed. The new algorithms only need to solve a linear equation in each step. For complementarity problems, the QR factorization on the quasi-Newton method is discussed.

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