"Flexible Penalty Functions for Nonlinear Constrained Optimization"
F. Curtis, J. Nocedal
IMA Journal on Numerical Analysis  (2008).

We propose a globalization strategy for nonlinear constrained optimization. The method employs a “flexible” penalty function to promote convergence, where during each iteration the penalty parameter can be chosen as any number within a prescribed interval, rather than a fixed value. This increased flexibility in the step acceptance procedure is designed to promote long productive steps for fast convergence. An analysis of the global convergence properties of the approach in the context of a line search Sequential Quadratic Programming method and numerical results for the KNITRO software package are presented.
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