University of Hertfordshire

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Geometric approach to Fletcher's ideal penalty function

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Original languageEnglish
Pages (from-to)433-441
JournalJournal of Optimization Theory and Applications
Publication statusPublished - 1995


In this note, we derive a geometric formulation of an ideal penalty function for equality constrained problems. This differentiable penalty function requires no parameter estimation or adjustment, has numerical conditioning similar to that of the target function from which it is constructed, and also has the desirable property that the strict second-order constrained minima of the target function are precisely those strict second-order unconstrained minima of the penalty function which satisfy the constraints. Such a penalty function can be used to establish termination properties for algorithms which avoid ill-conditioned steps. Numerical values for the penalty function and its derivatives can be calculated efficiently using automatic differentiation techniques.


Original article can be found at: Copyright Springer. [Originally produced as UH Technical Report 280, 1993]

ID: 90229