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Categorizing with Catastrophic Radii in Numerical Minimization

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Abstract

We introduce and develop a notion of “catastrophic radii” to identify where a minimization method may require an arbitrarily large number of steps to approximate a minimizer of an objective function, and we use this notion to categorize the performance of method/objective combinations. In order to investigate the different categories, we explore simple examples where explicit formulas can be used, and we discuss several ways that simulation can be used to investigate catastrophic radii for other method/objective combinations.

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Acknowledgments

I would like to thank the Referees and the Handling Editor for their very helpful comments that improved this paper.

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  1. Department of Mathematics, 8600 College Station, Bowdoin College, Brunswick, ME, 04011, USA

    Adam B. Levy

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  1. Adam B. Levy
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Correspondence to Adam B. Levy.

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Levy, A.B. Categorizing with Catastrophic Radii in Numerical Minimization. Set-Valued Var. Anal 29, 1–28 (2021). https://doi.org/10.1007/s11228-020-00534-4

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Mathematics Subject Classification (2010)

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