An Active Set-Type Newton Method for Constrained Nonlinear Systems
We consider the problem of finding a solution of a nonlinear system of equations subject to some box constraints. To this end, we introduce a new active set-type Newton method. This method is shown to be globally convergent in the sense that every accumulation point is a stationary point of a corresponding box constrained optimization problem. Moreover, the method is locally superlinearly or quadratically convergent under a suitable regularity condition. Furthermore the method generates feasible iterates and has to solve only one linear system of equations at each iteration. Due to our active set strategy, this linear system is of reduced dimension. Some preliminary numerical results are included.
KeywordsNonlinear equations box constraints Newton’s method active set strategy projected gradient global convergence quadratic convergence
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