Reformulating the Pascoletti-Serafini problem as a Bi-level optimization problem

We propose a new reformulation of the linear Pascoletti-Serafini problem as a bi-Level optimization problem. The Pascoletti-Serafini problem stands at the core of many Multi-Criteria Optimization problems, and in particular its linear version is used for navigation purposes on the Pareto frontier. The new reformulation is based on the split feasibility problem and thus enables us to apply projection methods. We show how Solodov's method can be applied to solving the equivalent bi-level optimization problem. The method is a projected gradient method, iteratively applied to a parametrized family of functions.