
Minimax Theory and its Applications 06 (2021), No. 2, 353364 Copyright Heldermann Verlag 2021 Duality Minimax and Applications Sofia Giuffrè D.I.I.E.S., Mediterranean University of Reggio Calabria, Reggio Calabria, Italy sofia.giuffre@unirc.it Attilio Marciano D.I.I.E.S., Mediterranean University of Reggio Calabria, Reggio Calabria, Italy The paper is devoted to the strong duality minimax theory, that works in infinite dimensional settings, and to its applications. In particular, we deal with the nonconstant gradient constrained problem and with the random traffic equilibrium problem. By means of this theory, we are able to show that, for both problems, the associated infinite dimensional variational inequalitiy on a convex feasible set is equivalent to a system of equations. Keywords: Duality theory, Lagrange multipliers, Nonconstant gradient constraints, Random traffic equilibrium problem. MSC: 49N15, 35J86, 49J55. [ Fulltextpdf (119 KB)] for subscribers only. 