A Lagrange multiplier expression method for bilevel polynomial optimization.
Bilevel optimization problem is a two-level optimization problem, where a subset of its variables is constrained in the optimizer set of another optimization problem parameterized by the remaining variables. In this talk, we introduce a Lagrange multiplier expression method for bilevel polynomial optimization based on polynomial optimization relaxations. Each relaxation is obtained from the Kurash-Kuhn-Tucker (KKT) conditions for the lower level optimization and the exchange technique for semi-infinite programming. The global convergence of the method is proved under some general assumptions. And some numerical examples will be given to show the efficiency of the method.