Characterization of local solutions for a class of nonconvex programs

A nonconvex programming problem, which arises in the context of application of Benders' decomposition procedure to a class of network optimization problems, is considered. Conditions which are both necessary and sufficient for a local maximum are derived. The concept of a basic local maximum is introduced, and it is shown that there is a finite number of basic local maxima and at least one such local maximum is optimal.