Journal of Convex Analysis, Vol. 5, No. 1, pp. 119-132 (1998)

Characterizations of Generalized
Monotone Nonsmooth Continuous Maps using Approximate Jacobians

V. Jeyakumar and D. T. Luc and S. Schaible

Department of Applied Mathematics, University of New South Wales, Sydney 2052, Australia, jeya@maths.unsw.edu.au, and Institute for Mathematics, Hanoi, Vietnam, dtluc@thevinh.ac.vn, and Graduate School of Management, University of California, Riverside, California, USA, schaible@ucrac1.ucr.edu

Abstract: This paper presents necessary and/or sufficient conditions for a continuous map to be monotone, quasimonotone or pseudomonotone. The results are given in terms of approximate Jacobian matrices which reduce to convexificators for a real-valued map. The results extend corresponding results obtained using Clarke generalized Jacobian matrices.

Keywords: Monotone maps, quasimonotone maps, pseudomonotone maps, approximate Jacobians

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