Abstract: It is known that for a strictly concave-convex function, the gradient method introduced by Arrow and Hurwicz [1], has guaranteed global convergence to its saddle point. Nevertheless, there ...

Given a separated dual system (E, E'), the Fenchel transform determines a pairing of the convex functions on E with the convex functions on E'. This operation is shown to have a continuity property.

A simple expression is presented that is equivalent to the norm of the $L_v^p \to L_u^q$ embedding of the cone of quasi-concave functions in the case 0 < q < p < ∞ ...