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 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 the first part of this paper we prove that the global quadratic optimization problem over a simplex can be solved with a constant relative accuracy. In the second part we consider some natural extensions of the result.

We present a convex conic relaxation for a problem of maximising an indefinite quadratic form over a set of convex constraints on the squared variables. We show that for all these problems we get at least 12/37 relative accuracy of the approximation. In the second part of the paper we derive the...

We present a survey of nondifferentiable optimization problems and methods with special focus on the analytic center cutting plane method. We propose a self-contained convergence analysis, that uses the formalism of the theory of self-concordant fucntions, but for the main results, we give...

The paper is a simplified exposition of an early combined phase I-phase II method for linear programming. The method works from an infeasible start. Besides, there is no need for regularity conditions if the method is applied to a primal-dual formulation.

In this paper the existence of unemployment is partly explaines as being the result of coordination failures. This is achieved by considering a standard general equilibrium modes and splitting the set of commodities in two groups. The first group contains commodities like gold. The prices of...

Given a compact connected component of zeros of a vector field, we give a necessary condition for its asymptotic stability in terms of its index and Euler characteristic.

In this paper, we prove an existence theorem for equilibria in production economies with increasing returns, which generalizes the classis results on this topic. In partular, we eliminate both the free-disposal assumptions and any smoothness requirements on the boundary of the production sets....

In this paper we consider a labor constrained scheduling problem (LCSP) which is a simplification of a practical problem arising in industry. Jobs are subject to precedence constraints and have specified processing times. Moreover, for each job the labor requirements varies as the job is...