Second order multipliers and marginal function in non linear programs

For finite dimensional Optimization problems, some first and second order constraints qualification conditon is proposed which draws the existence of the first and second order multipliers and some sufficient condition is given for the existence of first and second order Lagrange multipliers common to several critical directions. Realted results are stated concerning the value function of the programs. Under some Holderian stability assumption the existence of directional derivatives is proved and their expression is given by means of the first and second order Lagrange multipliers.