Overelaxed hit-and-run Monte Carlo for the uniform sampling of convex bodies with applications in metabolic network analysis

The uniform sampling of convex regions in high dimension is an important computational issue, from both theoretical and applied point of view. The hit-and-run montecarlo algorithms are the most efficient methods known to perform it and one of their bottlenecks relies in the difficulty of escaping from tight corners in high dimension. Inspired by optimized montecarlo methods used in statistical mechanics we define a new algorithm by overelaxing the hit-and-run dynamics. We made numerical simulations on high dimensional simplices in order to test its performances, pointing out its improved ability to escape from angles and finally apply it to an inference problem in the steady state dynamics of metabolic networks.