The equivalence of strict convexity and injectivity of the gradient in bounded level sets

Abstract:

It is shown that Lipschitzian functions are strictly convex if and only if their generalized gradients are disjoint at distinct interior points of a given bounded level set. © 1991 The Mathematical Programming Society, Inc.

Año de publicación:

1991

Keywords:

• affine invariance
• generalized gradient
• injectivity
• Convexity
• supporting hyperplane

Fuente:

scopus