Abstract
In this paper, optimization methods for hierarchical systems are dealt with. We consider a problem in which the upper level objective function includes the lower level optimal value function.
First, we review several useful results in sensitivity analysis which are already obtained by many resarchers. Moreover we point out that information on sensitivity analysis for optimal value function (i.e. gradient, generalized gradient or directional derivative) depends on the uniqueness of the optimal solution and of the Lagrange multiplier vector.
Next, under the uniqueness of optimal solution and Cottle constraint qualification, we consider a problem for finding the upper level descent direction. This problem is formulated as a quadratic programming problem. Therefore, we may apply a proper solution method to the problem to obtain the upper level descent direction.
Finally, we construct an optimization algorithm for the two-level hierarchical system based on the above results.
