Slopes and Moreau-Rockafellar Theorem

Properties of local and global slope of a function and its approximate critical points sets are studied in relation to determination of the function

GRADIENT FLOWS, SECOND-ORDER GRADIENT SYSTEMS AND CONVEXITY

We disclose an interesting connection between the gradient flow of a e(2)-smooth function psi and strongly evanescent orbits of the second-order gradient system defined by the square-norm of del psi under an adequate convexity assumption. As a consequence, we obtain the following surprising result for two C-2, convex, and bounded from below functions psi(1), psi(2) if parallel to del psi(1)parallel to = parallel to del psi(2)parallel to, then psi(1) = psi(2) + k for some k is an element of R