Characterization of the monotone polar of subdifferentials

Characterization of the monotone polar of subdifferentials

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Article ID: iaor2014858
Volume: 8
Issue: 5
Start Page Number: 1735
End Page Number: 1740
Publication Date: Jun 2014
Journal: Optimization Letters
Authors:
Keywords: graphs
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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