General necessary and sufficient conditions for constrained optimum problems (Q1337776)

Let \(D\) be an open set of a linear normed space \(X\), \(F: D\to X\) a continuous function and \(Q\) a prescribed subset of \(X\). One gives a necessary and sufficient condition (in terms of tangent maps) for \(x\) to be a local solution to the constrained problem: Minimize \(f(x)\) for \(x\in Q\cap D\).