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Characterization of the monotone polar of subdifferentials

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Abstract

We show that a point is solution of the Minty variational inequality of subdifferential type for a given lower semicontinuous function if and only if the function is increasing along rays starting from that point. This provides a characterization of the monotone polar of subdifferentials of lower semicontinuous functions: it is a common subset of their graphs which depends only on the function.

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  1. Université des Antilles et de la Guyane, 97159 , Pointe à Pitre, France

    Marc Lassonde

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  1. Marc Lassonde
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Correspondence to Marc Lassonde.

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Lassonde, M. Characterization of the monotone polar of subdifferentials. Optim Lett 8, 1735–1740 (2014). https://doi.org/10.1007/s11590-013-0693-7

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  • DOI: https://doi.org/10.1007/s11590-013-0693-7

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