DIRECTIONAL-DERIVATIVES OF OPTIMAL-SOLUTIONS IN SMOOTH NONLINEAR-PROGRAMMING

We consider a smooth nonlinear program subject to perturbations in the right-hand side of the constraints. We do not assume that the unique solution of the original problem satisfies any qualification hypothesis. We suppose instead that the direction of perturbation satisfies the hypothesis of Gollan. We study the variation of the cost and, with the help of some second-order sufficiency conditions, obtain some conditions satisfied by the first term of the expansion of the solution. These conditions may vary depending on the existence of a Lagrange multiplier for the original problem.