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The uniform sampling of convex regions in high dimension is an importantcomputational issue, from both theoretical and applied point of view. Thehit-and-run montecarlo algorithms are the most efficient methods known toperform it and one of their bottlenecks relies in the difficulty of escapingfrom tight corners in high dimension. Inspired by optimized montecarlo methodsused in statistical mechanics we define a new algorithm by overelaxing thehit-and-run dynamics. We made numerical simulations on high dimensionalsimplices in order to test its performances, pointing out its improved abilityto escape from angles and finally apply it to an inference problem in thesteady state dynamics of metabolic networks.

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