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A Discussion on Variational Analysis in Derivative-Free Optimization

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Abstract

Variational Analysis studies mathematical objects under small variations. With regards to optimization, these objects are typified by representations of first-order or second-order information (gradients, subgradients, Hessians, etc). On the other hand, Derivative-Free Optimization studies algorithms for continuous optimization that do not use first-order information. As such, researchers might conclude that Variational Analysis plays a limited role in Derivative-Free Optimization research. In this paper we argue the contrary by showing that many successful DFO algorithms rely heavily on tools and results from Variational Analysis.

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  1. Department of Mathematics, University of British Columbia, Kelowna, British Columbia, Canada

    Warren Hare

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Hare’s research is partially supported by Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant #2018-03865.

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Hare, W. A Discussion on Variational Analysis in Derivative-Free Optimization. Set-Valued Var. Anal 28, 643–659 (2020). https://doi.org/10.1007/s11228-020-00556-y

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