Abstract

Recent characterizations of various types of differentiable generalized monotone maps by Karamardian–Schaible–Crouzeix and their strengthened versions by Crouzeix–Ferland are extended to the nonsmooth case. For nondifferentiable locally Lipschitz maps necessary and/or sufficient conditions for quasimonotonicity, pseudomonotonicity and strict/ strong pseudomonotonicity are derived. To accomplish this, the generalized Jacobian in the sense of Clarke is employed.

Author information

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

Dinh The Luc

Institute of Mathematics, Hanoi, Vietnam.

S. Schaible

Graduate School of Management, University of California, Riverside, CA 92521, USA

Keywords

  • Monotone map
  • quasimonotone map
  • pseudomonotone map
  • generalized Jacobian

Suggested citation

Dinh The Luc, S. Schaible. “Generalized Monotone Nonsmooth Maps.” Journal of Convex Analysis 3 (1996), No. 2, 195–205. https://doi.org/10.68381/jca03013

Download BibTeXPublished by Heldermann Verlag.

Published by Heldermann Verlag, 1996. Rights now held by Banach Press.