Global optimization in arcwise connected metric spaces

Abstract

where M is an arcwise connected metric space and f is a functional on M. Standard algorithms for nonlinear finite programming, optimal control and approximation problems at most can approximate local minima off over M. Therefore the question of characterizing that family of functionals on M whose local minima are global is of considerable interest in optimization. An answer has been given in 111 for convex, compact finite-dimensional sets M (for previous approaches see the references in Ill). It is the purpose of this brief note to extend the results given in [ 11 to the case of arcwise connected metric spaces and to thereby cover certain classes of approximation and control problems.