Finding A Stable Solution of A System of Nonlinear Equations

This paper presents new methods for finding dynamically stable solutions of systems of nonlinear equations. The concepts of stability functions and the so-called stable solutions are defined. Based on those new concepts, two models of stable solutions and three stability functions are proposed. These stability functions are semismooth. Smoothing technology is applied to such stability functions. Smoothing Newton methods are proposed to solve the stable solution models. Convergence properties of these methods are studied. We report on numerical examples which illustrate the utility of the new approach.

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