A discrete problem can be relaxed by taking the continuous relaxation of an integer programming formulation An equivalent relaxation is obtained by projecting this relax ation onto the original continuous variables The projection is simple for piecewise linear functions xed charge problems and some disjunctive constraints This allows one to solve much smaller relaxations without sacri cing the ...

Spectral Clustering as a relaxation of the normalized/ratio cut has become one of the standard graph-based clustering methods. Existing methods for the computation of multiple clusters, corresponding to a balanced k-cut of the graph, are either based on greedy techniques or heuristics which have weak connection to the original motivation of minimizing the normalized cut. In this paper we propos...

A standard approach to solve Mixed Integer Linear Programs is to perform a global branch and bound search through all possible combinations. Due to the hardness of the problem, this search must be closely controlled by a constraint solver which uses constraints to prune the search space in an a priori way. In this paper, we deene a new domain reduction solver which uses in a cooperative way a s...