Sufficient Conditions for Global Minima of Suitably Convex Functionals from Variational and Control Theory

Abstract

A so-called semilocal convexity of integrals and of integrands is discussed in § 1, then used in § 2 in obtaining sufficiency theorems for global minima. The question of the possible use of such convexity in estimating the excess of a computed approximation $J(y_m )$ over the infimum of $J(y)$ is raised in § 4. A second approach to sufficiency for global minima based on the existence and uniqueness of a minimizing function is treated in § 3. Some simple examples are given in § 5.