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Stochastic programming

About: Stochastic programming is a research topic. Over the lifetime, 12343 publications have been published within this topic receiving 421049 citations.


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TL;DR: A broad class of stochastic dynamic programming problems that are amenable to relaxation via decomposition are considered, namely, Lagrangian relaxation and the linear programming (LP) approach to approximate dynamic programming.
Abstract: We consider a broad class of stochastic dynamic programming problems that are amenable to relaxation via decomposition. These problems comprise multiple subproblems that are independent of each other except for a collection of coupling constraints on the action space. We fit an additively separable value function approximation using two techniques, namely, Lagrangian relaxation and the linear programming (LP) approach to approximate dynamic programming. We prove various results comparing the relaxations to each other and to the optimal problem value. We also provide a column generation algorithm for solving the LP-based relaxation to any desired optimality tolerance, and we report on numerical experiments on bandit-like problems. Our results provide insight into the complexity versus quality trade-off when choosing which of these relaxations to implement.

187 citations

Journal ArticleDOI
TL;DR: The applications of stochastic processes to studying social mobility and flows of personnel within organizations receive much more extended treatment here than in other introductory treatments of applied stochastics processes.
Abstract: of the models analyzed include the spectral representation of solution vectors, limiting states, the covariance matrix of the elements of the state composition vector, the means and variances of sojourn times, and expanding and contracting systems, rather than methods of statistical estimation. In the discussion of discrete time models, the illustrations are drawn primarily from the study of social and occupational mobility, and for continuous time models, they are drawn from the field of educational and manpower planning. The remaining five chapters treat control theory for Markov models, models for duration and size, models for social systems with fixed class sizes, and simple and general epidemic models for the diffusion of news, rumors, and ideas. Simple epidemic models are birth process models that assume that infection is an irreversible state, so given either a constant individual rate of transmission or a single constant source of transmission, the entire population is eventually infected. General epidemic models allow for the duration of infection to be a random variable. The book ends with a full, up-to-date bibliography, an author index, and a subject index. In summary, Bartholomew gives an excellent introduction to many types of stochastic processes and a broad range of applications for modeling and planning social systems. The applications of stochastic processes to studying social mobility and flows of personnel within organizations receive much more extended treatment here than in other introductory treatments of applied stochastic processes. The "Complements" section at the end of each chapter is a useful overview of recent research investigations in many other areas of application that apply or extend the models presented in the chapter. Since no problems for solution are contained and the exposition is often informal, some teachers may wish to supplement the book with more traditional stochastic process textbooks, one good choice being Karlin and Taylor (1975). There seem to be few typographical errors.

187 citations

Journal ArticleDOI
TL;DR: Two variants of a new method for solving discrete stochastic optimization problems by generating a sequence taking values in the set of feasible alternatives, which is shown to converge almost surely to a globally optimal solution of the underlying optimization solution.
Abstract: This paper is concerned with the problem of optimizing the performance of a stochastic system over a finite set of alternatives in situations where the performance of the system cannot be evaluated analytically, but must be estimated or measured, for instance, through simulation. We present two variants of a new method for solving such discrete stochastic optimization problems. This new method uses global search to look for the optimal solution. It generates a sequence taking values in the set of feasible alternatives, where each new element of the sequence is generated by comparing the current element with another candidate alternative and letting the next element of the sequence be the one of the current and candidate alternatives that appears to yield better performance. For both versions of the proposed method, the element of the set of feasible alternatives that the generated sequence visits most often is shown to converge almost surely to a globally optimal solution of the underlying optimization pr...

187 citations

Journal ArticleDOI
TL;DR: Two types of methods for solving stochastic variational inequality problems (SVIP) where the underlying functions are the expected value of Stochastic functions based on projections and reformulations of SVIP are proposed.
Abstract: Stochastic approximation methods have been extensively studied in the literature for solving systems of stochastic equations and stochastic optimization problems where function values and first order derivatives are not observable but can be approximated through simulation. In this paper, we investigate stochastic approximation methods for solving stochastic variational inequality problems (SVIP) where the underlying functions are the expected value of stochastic functions. Two types of methods are proposed: stochastic approximation methods based on projections and stochastic approximation methods based on reformulations of SVIP. Global convergence results of the proposed methods are obtained under appropriate conditions.

187 citations

Journal ArticleDOI
TL;DR: In this paper, a robust optimization model for planning power system capacity expansion in the face of uncertain power demand is developed. But the model is not suitable for the case of large-scale power systems.
Abstract: We develop a robust optimization model for planning power system capacity expansion in the face of uncertain power demand. The model generates capacity expansion plans that are both solution and model robust. That is, the optimal solution from the model is ‘almost’ optimal for any realization of the demand scenarios (i.e. solution robustness). Furthermore, the optimal solution has reduced excess capacity for any realization of the scenarios (i.e. model robustness). Experience with a characteristic test problem illustrates not only the unavoidable trade-offs between solution and model robustness, but also the effectiveness of the model in controlling the sensitivity of its solution to the uncertain input data. The experiments also illustrate the differences of robust optimization from the classical stochastic programming formulation.

187 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023175
2022423
2021526
2020598
2019578
2018532