Directional derivative estimates for the optimal value function of a quasidifferentiable programming problem

This paper is concerned with the optimal value function arising in the primal decomposition of a quasidifferentiable programming problem. In particular, estimates for the upper Dini directional derivative of this function are derived. They involve certain ‘Lagrange multipliers’ occurring in the necessary minimum conditions to the lower level problems. This study generalizes some previously published results on this subject.