Titlebook: Generalized Convexity and Generalized Monotonicity; Proceedings of the 6 Nicolas Hadjisavvas,Juan Enrique Martínez-Legaz,Je Conference proc

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,Resource Management — Protection,lities. In particular, it is shown that the Minty variational inequality problem derived from a map . defined on a convex domain is solvable on any nonempty, compact, and convex subdomain if and only if . is properly quasimonotone.

Preamble

Normal Cones to Sublevel Sets: An Axiomatic Approach the definition given in [.] (resp. [.]) is recovered. Moreover, the results obtained in [.] are extended in this more general setting. Under mild assumptions, quasiconvex continuous functions are classified, establishing an equivalence relation between functions with the same normal operator. Applications in pseudoconvexity are also discussed.

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Stochastic ,-(increasing) Convexity of compound sums. This question is investigated here with respect to the class of stochastic .(increasing) convex orderings introduced recently. The analysis is based on a central property, called stochastic .(increasing) convexity, for families of parametric distributions.

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Fixed Point Theorems, Coincidence Theorems and Variational Inequalitiesult. A noncompact coincidence point theorem is also established. Applications of these results to establish the existence of solutions to variational inequalities in not necessarily reflexive Banach spaces are also considered.

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A Note on Minty Variational Inequalities and Generalized Monotonicitylities. In particular, it is shown that the Minty variational inequality problem derived from a map . defined on a convex domain is solvable on any nonempty, compact, and convex subdomain if and only if . is properly quasimonotone.

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https://doi.org/10.1007/978-1-4020-5608-6In the present paper we define weaker invexity-type properties and examine the relationships between the new concepts and other similar conditions. One obtains in this way necessary and sufficient conditions for Kuhn-Tucker sufficiency. Moreover one proves that the same conditions are sufficient for Wolfe duality.