Bilevel programming problems — theory, algorithms and applications to energy networks
- S. Dempe, V. Kalashnikov, G. A. Pérez-Valdés, N. Kalashnykova
We consider a bilevel programming problem. The leader’s objective function is assumed to be linear. The follower’s problem is a quantile minimization problem. It is assumed that the follower’s loss function is bilinear. We obtain a deterministic equivalent of the original problem in the case of a scalar random variable. In the case of the normal distribution of the random vector, an algorithm to solve the follower’s problem is suggested. We consider an economic model example to illustrate the suggested method. Results of computation are described.