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 Martínez-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, variational inequality problems and upper sign-continuity.

Keywords:

• Pseudomonotonicity
• maximal pseudomonotonicity
• pseudomonotone polarity
• variational inequalities

Acknowledgements

We would like to thank the anonymous referee for the suggestions, which helped to improve this work.

Notes

No potential conflict of interest was reported by the authors.