The Pseudomonotone Polar for Multivalued Operators

Abstract

In this work, we study the pseudomonotonicity of multivalued operators from the point of view of polarity, in an analogous way as the well-known monotone polar due to Mart\'inez-Legaz and Svaiter, and the quasimonotone polar recently introduced by Bueno and Cotrina. We show that this new polar, adapted for pseudomonotonicity, possesses analogous properties to the monotone and quasimonotone polar, among which are a characterization of pseudomonotonicity, maximality and pre-maximality. Furthermore, we characterize the notion of $D$-maximal pseudomonotonicity introduced by Hadjisavvas. We conclude this work studying the connections between pseudomonotonicity and variational inequality problems.