On the existence of Lagrange multipliers in nonlinear programming in Banach spaces

The existence of Lagrange-Karush-Kuhn-Tucker multipliers in differentiable mathematical programming is shown to be a direct consequence of fundamental rules for computing tangent cones. The relationships of these rules with the transversality conditions of differential topology are pointed out. These rules also bear some connections with subdifferential calculus for convex (or tangentially convex [20]) functions.

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