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The ABC of DC Programming

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Abstract

A function is called DC if it is expressible as the difference of two convex functions. In this work, we present a short tutorial on difference-of-convex optimization surveying and highlighting some important facts about DC functions, optimality conditions, and recent algorithms. The manuscript, accessible to a wide range of readers familiar with the convex analysis machinery, builds upon three pillars from variational analysis: directional derivative, ε-subdifferential, and the Legendre-Fenchel transform.

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Acknowledgements

The author thanks the editors of this special issue for their kind invitation, and two anonymous reviewers for their valuable remarks and careful reading. The author also acknowledges financial support from the Gaspard-Monge Program for Optimization and Operations Research (PGMO) project “Models for planning energy investment under uncertainty”.

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  1. CMA – Centre de Mathématiques Appliquées, MINES ParisTech, PSL – Research University, Sophia Antipolis, France

    Welington de Oliveira

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  1. Welington de Oliveira
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Correspondence to Welington de Oliveira.

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de Oliveira, W. The ABC of DC Programming. Set-Valued Var. Anal 28, 679–706 (2020). https://doi.org/10.1007/s11228-020-00566-w

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