Abstract

The Krylov subspace GMRES (m) method is the programming arithmetic based on the projection method. Now, it has become into the excellent arithmetic to solve the linear problem with large scale, and it also can be applied in the nonlinear programming problems. In this article, we translate the nonlinear optimization problems into the non-smooth equations to solve them. We put forward the iterative method of Newton-GMRES to solve the non-smooth equations, and for large-sized problem, this method is especially applied. And the samples also prove the validity of this method.

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