Problems dealing with the design and the operations of gas transmission networks are challenging. The difficulty mainly arises from the simultaneous modeling of gas transmission laws and of the investment costs. The combination of the two yields a non- linear non-convex optimization problem. To...

We propose an alternative approach to stochastic programming based on Monte-Carlo sampling and stochastic gradient optimization. The procedure is by essence probabilistic and the computed solution is a random variable. The associated objective value is doubly random, since it depends on two...

In this paper we consider a new analytic center cutting plane method in a projective space. We prove the efficiency estimates for the general scheme and show that these results can be used in the analysis of a feasibility problem, the variational inequality problem and the problem of constrained...

We present a variant of the Cholesky factorization for block tridiagonal positive definite matrices. We show that a suitable ordering of block pivots makes it possible to parallelize the linear algebra on a multiple instruction multiple data (MIMD) processor achitecture. The technique applies to...

This paper proposes a Benders-like partitioning algorithm to solve the network loading problem. The effort of computing integer solutions is entirely left to a pure integer programming solver while valid inequalities are generated by solving standard nonlinear multicommodity flow problems. The...

Problems dealing with the design and the operations of gas transmission networks arechallenging. The difficulty mainly arises from the simultaneous modeling of gastransmission laws and of the investment costs. The combination of the two yields a nonlinearnon-convex optimization problem. To...