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

: Gibali, A.; Küfer, K.-H.; Süss, P.

Reich, S. ; American Mathematical Society -AMS-:
Infinite products of operators and their applications : A research workshop of the Israel Science Foundation, May 21 - 24, 2012, Haifa, Israel
Providence, RI: AMS, 2015 (Contemporary Mathematics 636)
ISBN: 978-1-4704-1480-1 (Print)
ISBN: 978-1-4704-2275-2 (Online)
DOI: 10.1090/conm/636/12731
Research Workshop on Infinite Products of Operators and their Applications <2012, Haifa>
Conference Paper
Fraunhofer ITWM ()

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.