Getting Feasible Variable Estimates from Infeasible Ones: MRF Local Polytope Study

This paper proposes a method for the construction of approximate feasible primal solutions from infeasible ones for large-scale optimization problems possessing certain separability properties. Whereas the infeasible primal estimates can typically be produced from (sub-) gradients of the dual function, it is often not easy to project them to the primal feasible set, since the projection itself has a complexity comparable to the complexity of the initial problem. We propose an alternative efficient method to obtain feasibility and show that its properties influencing the convergence to the optimum are similar to the properties of the Euclidean projection. We apply our method to the local polytope relaxation of inference problems for Markov Random Fields and discuss its advantages over existing methods.