Necessary optimality conditions for an optimization problem with equality constraint

Abstract

A simple algebraic condtion on the intrinsic derivative ⊢;² f(a) of a differentiable map f at a point n is shown to assure identification between the contingent cone at x of the level surface W through a and the null cone of ⊢² f(a). We exploit this fact for finding necessary optimality conditions of first and second order for a differentiable functional J on W at a

Keywords:

• Contingent Cone
• Equality Constraint
• Local Minimum
• Diret Morphism
• Section