REGULARITY AND STABILITY FOR THE MATHEMATICAL-PROGRAMMING PROBLEM IN BANACH-SPACES

This paper deals with a regularity assumption for the mathematical programming problem in Banach spaces. The attractive feature of our constraint qualification is the fact that it can be considered as a condition on the active part only of the constraint, and that it is preserved under small perturbations. Moreover, we show that our condition is almost" equivalent to the existence of a non-empty and weakly compact set of Lagrange multipliers. The main step in the proof of our results is a generalization of the open mapping theorem. © 1979 Springer-Verlag New York Inc."