Working with Ellipsoidal Uncertainty (Machine Learning)

Abstract: This work addresses the Robust counterpart of the Shortest Path Problem (RSPP) with a correlated uncertainty set. Since this problem is hard, a heuristic approach, based on Frank-Wolfe's algorithm named Discrete Frank-Wolf (DFW), has recently been proposed. The aim of this paper is to propose a semi-definite programming relaxation for the RSPP that provides a lower bound to validate approaches such as DFW Algorithm. The relaxed problem results from a bidualization that is done {through} a reformulation of the RSPP into a quadratic problem. Then the relaxed problem is solved using a sparse version of Pierra's decomposition in a product space method.