Stability in the stochastic programming
Stability of stochastic optimization problems - nonmeasurable case
This paper deals with stability of stochastic optimization problems in a general setting. Objective function is defined on a metric space and depends on a probability measure which is unknown, but, estimated from empirical observations. We try to derive stability results without precise knowledge of problem structure and without measurability assumption. Moreover, -optimal solutions are considered. The setup is illustrated on consistency of a --estimator in linear regression model.
Stochastic algorithms for buffer allocation in reliable production lines.
Stochastic bottleneck transportation problem with flexible supply and demand quantity
We consider the following bottleneck transportation problem with both random and fuzzy factors. There exist supply points with flexible supply quantity and demand points with flexible demand quantity. For each supply-demand point pair, the transportation time is an independent positive random variable according to a normal distribution. Satisfaction degrees about the supply and demand quantity are attached to each supply and each demand point, respectively. They are denoted by membership functions...
Stochastic dynamic programming applied to hydrothermal power systems operation planning based on the convex hull algorithm.
Stochastic dynamic programming with random disturbances
Several peculiarities of stochastic dynamic programming problems where random vectors are observed before the decision ismade at each stage are discussed in the first part of this paper. Surrogate problems are given for such problems with distance properties (for instance, transportation problems) in the second part.
Stochastic geometric programming with an application
In applications of geometric programming, some coefficients and/or exponents may not be precisely known. Stochastic geometric programming can be used to deal with such situations. In this paper, we shall indicate which stochastic programming approaches and which structural and distributional assumptions do not destroy the favorable structure of geometric programs. The already recognized possibilities are extended for a tracking model and stochastic sensitivity analysis is presented in the context...
Stochastic goal programming wth recourse
In this article we discuss several alternative formulations for Stochastic Goal Programming. Only one of these models, which is a particular case of the Stochastic Programs with Recourse, is also compatible with Bayesian Decision Theory. Moreover, it is posible to approximate its solutions by means of an iterative algorithm.
Stochastic optimization problems with second order stochastic dominance constraints via Wasserstein metric
Optimization problems with stochastic dominance constraints are helpful to many real-life applications. We can recall e. g., problems of portfolio selection or problems connected with energy production. The above mentioned constraints are very suitable because they guarantee a solution fulfilling partial order between utility functions in a given subsystem of the utility functions. Especially, considering (where is a system of non decreasing concave nonnegative utility functions) we obtain...
Stochastische dynamische Optimierung als Spezialfall linearer Optimierung in halbgeordneten Vektorräumen.
Stratified filtered sampling in stochastic optimization.
Thin and heavy tails in stochastic programming
Optimization problems depending on a probability measure correspond to many applications. These problems can be static (single-stage), dynamic with finite (multi-stage) or infinite horizon, single- or multi-objective. It is necessary to have complete knowledge of the “underlying” probability measure if we are to solve the above-mentioned problems with precision. However this assumption is very rarely fulfilled (in applications) and consequently, problems have to be solved mostly on the basis of...
Three Digit Accurate Multiple Normal Probabilities.
Tractable algorithms for chance-constrained combinatorial problems
This paper aims at proposing tractable algorithms to find effectively good solutions to large size chance-constrained combinatorial problems. A new robust model is introduced to deal with uncertainty in mixed-integer linear problems. It is shown to be strongly related to chance-constrained programming when considering pure 0–1 problems. Furthermore, its tractability is highlighted. Then, an optimization algorithm is designed to provide possibly good solutions to chance-constrained combinatorial...
Two-stage stochastic programming approach to a PDE-constrained steel production problem with the moving interface
The paper is concerned with a parallel implementation of the progressive hedging algorithm (PHA) which is applicable for the solution of stochastic optimization problems. We utilized the Message Passing Interface (MPI) and the General Algebraic Modelling System (GAMS) to concurrently solve the scenario-related subproblems in parallel manner. The standalone application combining the PHA, MPI, and GAMS was programmed in C++. The created software was successfully applied to a steel production problem...
Über einfache Mannigfaltigkeiten im linearen affinen Raum in globaler Auffassung
Warm-start cuts for Generalized Benders Decomposition
In this paper, we describe a decomposition algorithm suitable for two-stage convex stochastic programs known as Generalized Benders Decomposition. For this algorithm we propose a new reformulation that incorporates a lower bound cut that serves as a warm-start, decreasing the overall computation time. Additionally, we test the performance of the proposed reformulation on two modifications of the algorithm (bunching and multicut) using numerical examples. The numerical part is programmed in MATLAB...
Вероятностное вогнутое динамическое программирование