期刊
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
卷 45, 期 2, 页码 209-236出版社
SPRINGER
DOI: 10.1007/s10589-009-9240-y
关键词
Nonlinear programming; Augmented Lagrangians; Global convergence; Optimality conditions; Second-order conditions; Constraint qualifications
A Nonlinear Programming algorithm that converges to second-order stationary points is introduced in this paper. The main tool is a second-order negative-curvature method for box-constrained minimization of a certain class of functions that do not possess continuous second derivatives. This method is used to define an Augmented Lagrangian algorithm of PHR (Powell-Hestenes-Rockafellar) type. Convergence proofs under weak constraint qualifications are given. Numerical examples showing that the new method converges to second-order stationary points in situations in which first-order methods fail are exhibited.
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