A New Approach to Solve Convex Infinite Dimensional Bilevel Problems: Application to the Pollution Emission Price Problem

This paper presents a new approach to studying bilevel programming problems in infinite dimensional spaces, based on infinite dimensional duality and evolutionary variational inequalities. The result is applied to the evolutionary emission price problem. In our model, the government chooses the optimal price of pollution emissions, with consideration to firms' response to the price. Moreover, firms choose the optimal quantities of production to maximize their profits, given the price of pollution emissions. Finally, we provide a numerical example to show the feasibility of our approach.