Fabián Flores-Bazán, Fernando Flores-Bazán, A notion of conjugacy for nonconvex set-valued mappings of the real-line and related properties, Vol. 2022 (2022), Article ID 8, pp. 1-12

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DOI: 10.23952/cot.2022.8

Received July 23 2021; Accepted July 22, 2022; Published August 16, 2022

Abstract. Given a nonconvex set-valued mappings $F:\mathbb{R}^N\rightrightarrows \mathbb{R}$ , a notion of conjugate $F^{*}$ is introduced with the goal that $(F^{*})^*=F$ . This is given by using the usual (bilinear) duality pairing. Several examples showing its geometric interpretation are presented, as well as a notion of subdifferential for such set-valued maps is also outlined.

How to Cite this Article:
F. Flores-Bazán, F. Flores-Bazán, A notion of conjugacy for nonconvex set-valued mappings of the real-line and related properties, Commun. Optim. Theory 2022 (2022) 8.