Abstract

Recently pseudomonotone variational inequalities have been studied quite extensively, hereby extending the theory of pseudoconvex minimization problems. The focus of the present work are "pseudoaffine maps", i.e., pseudomonotone maps T for which -T is also pseudomonotone. A particular case of such maps are the gradients of pseudolinear functions. Our main goal is to derive the general form of pseudoaffine maps which are defined on the whole space.

Author information

Contact details are reproduced from the original publication and may be historical.

Monica Bianchi

Istituto di Econometria e Matematica per le Decisioni Economiche, Universita
Cattolica, Via Necchi 9, 20123 Milano, Italy

mbianchi@mi.unicatt.it

Nicolas Hadjisavvas

Dept. of Product and Systems Design, University of the Aegean, 84100 Hermoupolis, Syros, Greece

nhad@aegean.gr

Siegfried Schaible

A. G. Anderson Graduate School of Management, University of California, Riverside, CA 92521-0203,
U.S.A.

siegfried.schaible@ucr.edu

Keywords

  • Pseudoconvex function
  • pseudolinear function
  • pseudomonotone map
  • pseudoaffine map

Mathematics Subject Classification

26B25, 47N10, 47H99

Suggested citation

M. Bianchi, N. Hadjisavvas, S. Schaible. “On Pseudomonotone Maps T for which -T is also Pseudomonotone.” Journal of Convex Analysis 10 (2003), No. 1, 149–168.

Copyright Heldermann Verlag 2003