Nonsmooth Duality, Sandwich, and Squeeze Theorems
Adrian S. Lewis, Roberto Lucchetti · SIAM Journal on Control and Optimization · 2000
Given a nonlinear function h separating a convex and a concave function, we provide various conditions under which there exists an affine separating function whose graph is somewhere almost parallel to the graph of h. Such results blend Fenchel duality with a variational principle and are closely related to the Clarke--Ledyaev mean value inequality.