On the Existence of Lagrange Multipliers

Abstraact. This paper is devoted to discuss the existence of Lagrange multiplier for an optimal solution of the nonlinear programming problem treated by J. Zowe and S. Kurcyucz. An condition, which is slighty stronger than the regularity condition introduced by them, guarantee the existence of Kuhn-Tucker vector for the optimal solution, even if the image space of constrained map is not complete. Moreover, a necessary condition of the Fritz-John style is given, under conditions introducd while the existence of Kuhn-Tucker vector is being followed.