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On the local and global convergence of a reduced quasi-Newton method. (English) Zbl 0676.90061

Summary: In optimization in \({\mathbb{R}}^ n\) with m nonlinear equality constraints, we study the local convergence of reduced quasi-Newton methods, in which the updated matrix is of order n-m. Furthermore, we give necessary and sufficient conditions for superlinear convergence (in one step) and we introduce a device to globalize the local algorithm. It consists in determining a step along an arc in order to decrease an exact penalty function and we give conditions so that asymptotically the step-size will be equal to one.

MSC:

90C30 Nonlinear programming
65K05 Numerical mathematical programming methods
49M30 Other numerical methods in calculus of variations (MSC2010)
49M05 Numerical methods based on necessary conditions
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