On strong pseudomonotone and strong quasimonotone maps

Abstract

We introduce strong pseudomonotone and strong quasimonotone maps of higher order and establish their relationships with strong pseudoconvexity and strong quasiconvexity of higher order, respectively, which yields first-order characterizations of strong pseudoconvex and strong quasiconvex functions of higher order. Moreover, we answer the open problem (converse part of Proposition 6.2) of Karamardian and Schaible (J. Optim. Theory Appl. 66:37–46,1990), for even more generalized functions, namely strongly pseudoconvex functions of higher order. © Springer Nature Singapore Pte Ltd. 2018.