In this paper we present a solution method for stochastic integer problems. The method is a Benderstype algorithm that sequentially approximates the nonconvex recourse functions defined by the second stage subproblems. The presented convexification takes into account the domain that is induced by the collection of tender variables. The method is applied to a broad collection of stochastic integ...

In many applications of stochastic programming there is some uncertainty about the probability distribution P of the random parameters. The incomplete knowledge of the probability distribution can be described by assuming that P belongs to a specified class P of probability distributions. This in turn suggests to use the minimax decision rule. The first results were concerned with stochastic li...

In this paper we study stability of optimal solutions of stochastic programming problems with fixed recourse. An upper bound for the rate of convergence is given in terms of the objective functions of the associated deterministic problems. As an example it is shown how it can be applied to derivation of the Law of Iterated Logarithm for the optimal solutions. It is also shown that in the case o...

We introduce stochastic integer programs with dominance constraints induced by mixed-integer linear recourse. Closedness of the constraint set mapping with respect to perturbations of the underlying probability measure is derived. For discrete probability measures, large-scale, block-structured, mixed-integer linear programming equivalents to the dominance constrained stochastic programs are id...

In this paper we propose a new approach to fuzzy stochastic integrals of Itô and Aumann type. Then a fuzzy equation with fuzzy stochastic integrals is investigated. The existence and uniqueness of solution is proven. Some typical properties of the solution are also obtained. Similar results to set-valued stochastic integral equations are stated.

In this paper, stability of the optimal solution of stochastic programs with recourse with respect to parameters of the given distribution of random coefficients is studied. Provided that the set of admissible solutions is defined by equa[ity constraints only, asymptotical normality of the optimal solution follows by standard methods, If nonnegativity constraints are taken into account the prob...

We consider barrier problems associated with two and multistage stochastic convex optimization problems. We show that the barrier recourse functions at any stage form a selfconcordant family with respect to the barrier parameter. We also show that the complexity value of the first stage problem increases additively with the number of stages and scenarios. We use these results to propose a proto...

We consider the problem of approximating the expected recourse function for two-stage stochastic programs. Our problem is motivated by applications which have special structure such as an underlying network which allows reasonable approximations to the expected recourse function to be developed. In this paper, we show how these approximations can be improved by combining them with sample gradie...

Abstract In several real-world applications, modelled by two-stage stochastic problems, first and second-stage decisions (or some of their components) represent identical variables of the problem that is modelled. In these cases an appropriate solution of the problem might require that the second-stage decisions do not differ substantially from the corresponding first-stage ones. In this paper ...

A parallel inexact Newton method with a line search is proposed for two-stage quadratic stochastic programs with recourse. A lattice rule is used for the numerical evaluation of multi-dimensional integrals, and a parallel iterative method is used to solve the quadratic programming subproblems. Although the objective only has a locally Lipschitz gradient, global convergence and local superlinear...