Characterization of the monotone polar of subdifferentials

preprint2013arXivOpen access

Abstract

We show that a point is solution of the Minty variational inequality of subdifferential type for a given 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, which happens to be a common subset of their graphs depending only on the function.

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