EXPLICIT DETERMINATION OF A CONTINGENT CO NE - APPLICATION TO OPTIMIZATION

A simple algebraic condition on the intrinsic derivative Delta(2) f (a ) of a differentiable map f at a point a is shown to ensure identifica tion between the contingent cone at a of the level surface W of f thro ugh a and the null cone of Delta(2) f (a). We exploit this fact in ord er to find necessary optimality conditions of first and second orders for a differentiable functional J on W at a.