We propose an alternative apporach 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 objectiev value is doubly random, since it depends two...

In this paper we consider a homogeneous analytic center cutting plabne method in a projective space. We describe a general scheme that uses a homogeneous oracle and computes an approximate analytic center at each iteration. This technique is applied to a convex feasibility problem, to...

In this paper we present several "infeasible-start" path-following and potential-reduction primal-dual interior-point methods for non-linear conic problems. These methods try to find a recession direction of the feasible set of a self-dual homogeneous primal-dual problem.

In this paper we study the concepts of equilibrium and optimum in static transportation networks with elastic and non-elastic demands. The main mathematical tool of our paper is the theory of variational inequalities. We demonstrate that this theory is useful for proving the existence theorems....

In this paper we consider a new analytic center cutting plane method in a projective space. We prove the efficiency estimates for the general schemeand 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 new class of transportation systems, the stable dynamics models, which provides a natural link between the static and dynamic traffic network models. They can be seen as steady states of dynamic networks (flows are constant in time). These models turn out to be very easy to study...