We consider nonlinear stochastic optimization problems with probabilistic constraints. The concept of a p-efficient point of a probability distribution is used to derive equivalent problem formulations, and necessary and sufficient optimality conditions. We analyze the dual functional and its...

In this paper, an interior-point based global filtering algorithm is proposed to solve linear programming problems with the right-hand-side and cost vectors being stochastic. Previous results on the limiting properties of the Kalman filtering process have been extended to handle some...

In this paper, we consider optimization problems under probabilistic constraints which are defined by two-sided inequalities for the underlying normally distributed random vector. As a main step for an algorithmic solution of such problems, we prove a derivative formula for (normal)...

We discuss in this paper statistical inference of sample average approximations of multistage stochastic programming problems. We show that any random sampling scheme provides a valid statistical lower bound for the optimal (minimum) value of the true problem. However, in order for such lower...

Solutions of portfolio optimization problems are often influenced by errors or misspecifications due to approximation, estimation and incomplete information. Selected methods for analysis of results obtained by solving stochastic programs are presented and their scope illustrated on generic...

Expected recourse functions in linear two-stage stochastic programs with mixed-integer second stage are approximated by estimating the underlying probability distribution via empirical measures. Under mild conditions, almost sure uniform convergence of the empirical means to the original...

The guaranteed service model (GSM) computes optimal order-points in multi-echelon inventory control under the assumptions that delivery times can be guaranteed and the demand is bounded. Our new stochastic guaranteed service model (SGSM) with Recourse covers also scenarios that violate these...

We consider capacity expansion of a telecommunications network in the face of uncertain future demand and potential future failures of network components. The problem is formulated as a bicriteria stochastic program with recourse in which the total cost of the capacity expansion and the...

The main thrust of this study is the operational scheduling of the continuous coal handling and blending processes when considering multiple, and sometimes conflicting, objectives. A widely applicable generic goal programming model is proposed. Furthermore, assumptions regarding the certainty of...

The mean-risk stochastic mixed-integer programs can better model complex decision problems under uncertainty than usual stochastic (integer) programming models. In order to derive theoretical results in a numerically tractable way, the contamination technique is adopted in this paper for the...