zbMATH — the first resource for mathematics

An active set-type Newton method for constrained nonlinear systems. (English) Zbl 0983.90060
Ferris, Michael C. (ed.) et al., Complementarity: applications, algorithms and extensions. Papers from the international conference on complementarity (ICCP 99), Madison, WI, USA, June 9-12, 1999. Dordrecht: Kluwer Academic Publishers. Appl. Optim. 50, 179-200 (2001).
Summary: 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.
For the entire collection see [Zbl 0966.00043].

90C30 Nonlinear programming
90C53 Methods of quasi-Newton type