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Some brief observations in minimizing the sum of locally Lipschitzian functions

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Abstract

This works investigates a conceptual algorithm for computing critical points of nonsmooth nonconvex optimization problems whose objective function is the sum of two locally Lipschitzian (component) functions. We show that upon additional assumptions on the component functions and or feasible set, the given algorithm extends several well-known optimization methods.

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Notes

  1. Such an assumption is minimal for minimization of a function to be meaningful in the first place.

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Acknowledgements

We would like to thank three anonymous reviewers for their valuable time and interesting comments.

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Authors and Affiliations

  1. EDF R&D OSIRIS, 7, Boulevard Gaspard Monge, 91120, Palaiseau Cedex, France

    Wim van Ackooij

  2. MINES ParisTech, PSL - Research University, CMA - Centre de Mathématiques Appliquées, Sophia Antipolis, France

    Welington de Oliveira

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  1. Wim van Ackooij
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  2. Welington de Oliveira
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Correspondence to Wim van Ackooij.

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van Ackooij, W., de Oliveira, W. Some brief observations in minimizing the sum of locally Lipschitzian functions. Optim Lett 14, 509–520 (2020). https://doi.org/10.1007/s11590-019-01477-y

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