In this paper we develop a new theory of static equilibrium in congested transportation networks. Our considerations are based on a physical meaning of the flows rather than on an artificially chosen model of travel time functionsl We introduce a concept of the stable equilibrium and prove the...

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.

In this paper we develop new primal-dual interior-point methods for linear programming, which are based on the concept of parabolic target space. We show that such schemes work in the infinity-neighborhood of the primal-dual central path. Nevertheless these methods possess the best known...