Necessary Conditions for Bilevel Dynamic Optimization Problems
Jane J. Ye · SIAM Journal on Control and Optimization · 1995
In this paper we study the bilevel dynamic optimization problem, which is a hierarchy of two optimization problems where the constraint region of the upper-level problem is determined implicitly by the solution to the lower-level problem and where the upper-level decision variable is a vector while the lower-level decision variable is an admissible control function. To obtain optimality conditions, we reformulate the bilevel dynamic optimization problem as a single-level optimal control problem that involves the value function of the lower-level problem. A sensitivity analysis of the lower-level problem with respect to the perturbation in the upper-level decision variable is given, and the first-order necessary optimality conditions are derived by using nonsmooth analysis.