Abstract
AbstractThe main result is an equality type mean value theorem for tangentially convex functions in terms of tangential subdifferentials, which generalizes the classical one for differentiable functions, as well as Wegge theorem for convex functions. The new mean value theorem is then applied, analogously to what is done in the classical case, to characterize, in the tangentially convex context, Lipschitz functions, increasingness with respect to the ordering induced by a closed convex cone, convexity, and quasiconvexity.
Funder
Ministerio de Ciencia, Innovación y Universidades
Universitat Autònoma de Barcelona
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Geometry and Topology,Numerical Analysis,Statistics and Probability,Analysis
Reference30 articles.
1. Allevi, E., Martínez-Legaz, J.E., Riccardi, R.: Optimality conditions for convex problems on intersections of non necessarily convex sets. J. Glob. Optim. 77, 143–155 (2020)
2. Aussel, D., Corvellec, J.-N., Lassonde, M.: Subdifferential characterization of quasiconvexity and convexity. J. Convex Anal. 1, 195–201 (1994)
3. Avriel, M., Diewert, W.E., Schaible, S., Zang, I.: Generalized Concavity. Plenum Press, New York (1988)
4. Berge, C.: Espaces Topologiques. Fonctions Multivoques. Dunod, Paris (1966)
5. Clarke, F.H.: Necessary Conditions for Nonsmooth Problems in Optimal Control and the Calculus of Variations, Ph.D. thesis, Univ. of Washington (1973)
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献