Continuity and Differentiability of Quasiconvex Functions
Jean-Pierre Crouzeix · Kluwer Academic Publishers eBooks · 2006
The convexity of the epigraph of a convex function induces important properties with respect to the continuity and differentiability of the function. Moreover, the function is locally Lipschitz in the interior of the domain of the function. If for a quasiconvex function, the convexity concerns the lower level sets and not the epigraph, some important properties on continuity and differentiability are still preserved. An important property of quasiconvex functions is that they are locally nondecreasing with respect to some positive cone.