On regularity for constrained extremum problems. I: Sufficient optimality conditions (Q1035895)

The authors give equivalent conditions for the existence of a regular resp. a F.-John saddle point in terms of regular resp. linear separation of two sets in the image space of the objective function of a constrained optimization problem. The existence of a saddle point is a sufficient condition for a global optimum. This condition is compared with the calmness condition and metric regularity. The results are illustrated with a number of interesting examples.