Pascal Benchimol

We consider a resource allocation problem involving a large number of agents with individual constraints subject to privacy, and a central operator whose objective is to optimize a global, possibly nonconvex, cost while satisfying the…

We consider a resource allocation problem involving a large number of agents with individual constraints subject to privacy, and a central operator whose objective is to optimizing a global, possibly non-convex, cost while satisfying the…

We prove that primal-dual log-barrier interior point methods are not strongly polynomial, by constructing a family of linear programs with $3r+1$ inequalities in dimension $2r$ for which the number of iterations performed is in…

Unit commitment problem on an electricity network consists in choosing the production plan of the plants (units) of a company in order to meet demand constraints. It is generally solved using a decomposition approach where demand…

We disprove a continuous analogue of the Hirsch conjecture proposed by Deza, Terlaky and Zinchenko, by constructing a family of linear programs with $3r+4$ inequalities in dimension $2r+2$ where the central path has a total curvature in…

A combinatorial simplex algorithm is an instance of the simplex method in which the pivoting depends on combinatorial data only. We show that any algorithm of this kind admits a tropical analogue which can be used to solve mean payoff…

We develop a tropical analog of the simplex algorithm for linear programming. In particular, we obtain a combinatorial algorithm to perform one tropical pivoting step, including the computation of reduced costs, in O(n(m+n)) time, where m…

We introduce an algorithm which solves mean payoff games in polynomial time on average, assuming the distribution of the games satisfies a flip invariance property on the set of actions associated with every state. The algorithm is a…