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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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Journal ArticleDOI
TL;DR: The purpose of this overview is to discuss main theoretical results, some applications, and solution methods for this interesting and important class of programming problems.
Abstract: Mathematical programming problems dealing with functions, each of which can be represented as a difference of two convex functions, are called DC programming problems. The purpose of this overview is to discuss main theoretical results, some applications, and solution methods for this interesting and important class of programming problems. Some modifications and new results on the optimality conditions and development of algorithms are also presented.

657 citations

Journal ArticleDOI
TL;DR: In this article, an efficient method based on linear programming for approximating solutions to large-scale stochastic control problems is proposed. But the approach is not suitable for large scale queueing networks.
Abstract: The curse of dimensionality gives rise to prohibitive computational requirements that render infeasible the exact solution of large-scale stochastic control problems. We study an efficient method based on linear programming for approximating solutions to such problems. The approach "fits" a linear combination of pre-selected basis functions to the dynamic programming cost-to-go function. We develop error bounds that offer performance guarantees and also guide the selection of both basis functions and "state-relevance weights" that influence quality of the approximation. Experimental results in the domain of queueing network control provide empirical support for the methodology.

643 citations

Book
01 Jan 1971
TL;DR: In this article, a detailed treatment of the simpler problems, and filling the need to introduce the student to the more sophisticated mathematical concepts required for advanced theory by describing their roles and necessity in an intuitive and natural way.
Abstract: : The text treats stochastic control problems for Markov chains, discrete time Markov processes, and diffusion models, and discusses method of putting other problems into the Markovian framework. Computational methods are discussed and compared for Markov chain problems. Other topics include the fixed and free time of control, discounted cost, minimizing the average cost per unit time, and optimal stopping. Filtering and conrol for linear systems, and stochastic stability for discrete time problems are discussed thoroughly. The book gives a detailed treatment of the simpler problems, and fills the need to introduce the student to the more sophisticated mathematical concepts required for advanced theory by describing their roles and necessity in an intuitive and natural way. Diffusion models are developed as limits of stochastic difference equations and also via the stochastic integral approach. Examples and exercises are included. (Author)

643 citations

Journal ArticleDOI
TL;DR: In this paper, an integrated series of operations research studies directed toward improvement in such scheduling methods is presented. But the focus is on essentials of the mathematical model and other phases of the OR studies are brought in only as required.
Abstract: Scheduling heating oil production is an important management problem. It is also a complex one. Weather and demand uncertainties, allocation of production between different refineries, joint-and by-product relations, storage limitations, maintenance of minimal supplies and many other factors need to be considered. This paper is concerned with one of an integrated series of operations research studies directed toward improvement in such scheduling methods. Emphasis is on essentials of the mathematical model. Institutional features and other phases of the OR studies are brought in only as required.

632 citations

Book
01 Jan 2002
TL;DR: Pardalos and Resende as mentioned in this paper proposed a method to solve the problem of finding the minimum-cost single-Commodity Flow (MCSF) in a network.
Abstract: PrefacePanos M. Pardalos and Mauricio G. C. Resende: IntroductionPanos M. Pardalos and Mauricio G. C. Resende: Part One: Algorithms 1: Linear Programming 1.1: Tamas Terlaky: Introduction 1.2: Tamas Terlaky: Simplex-Type Algorithms 1.3: Kees Roos: Interior-Point Methods for Linear Optimization 2: Henry Wolkowicz: Semidefinite Programming 3: Combinatorial Optimization 3.1: Panos M. Pardalos and Mauricio G. C. Resende: Introduction 3.2: Eva K. Lee: Branch-and-Bound Methods 3.3: John E. Mitchell: Branch-and-Cut Algorithms for Combinatorial Optimization Problems 3.4: Augustine O. Esogbue: Dynamic Programming Approaches 3.5: Mutsunori Yagiura and Toshihide Ibaraki: Local Search 3.6: Metaheuristics 3.6.1: Bruce L. Golden and Edward A. Wasil: Introduction 3.6.2: Eric D. Taillard: Ant Systems 3.6.3: John E. Beasley: Population Heuristics 3.6.4: Pablo Moscato: Memetic Algorithms 3.6.5: Leonidas S. Pitsoulis and Mauricio G. C. Resende: Greedy Randomized Adaptive Search Procedures 3.6.6: Manuel Laguna: Scatter Search 3.6.7: Fred Glover and Manuel Laguna: Tabu Search 3.6.8: E. H. L. Aarts and H. M. M. Ten Eikelder: Simulated Annealing 3.6.9: Pierre Hansen and Nenad Mladenovi'c: Variable Neighborhood Search 4: Yinyu Ye: Quadratic Programming 5: Nonlinear Programming 5.1: Gianni Di Pillo and Laura Palagi: Introduction 5.2: Gianni Di Pillo and Laura Palagi: Unconstrained Nonlinear Programming 5.3: Constrained Nonlinear Programming }a Gianni Di Pillo and Laura Palagi 5.4: Manlio Gaudioso: Nonsmooth Optimization 6: Christodoulos A. Floudas: Deterministic Global Optimizatio and Its Applications 7: Philippe Mahey: Decomposition Methods for Mathematical Programming 8: Network Optimization 8.1: Ravindra K. Ahuja, Thomas L. Magnanti, and James B. Orlin: Introduction 8.2: Ravindra K. Ahuja, Thomas L. Magnanti, and James B. Orlin: Maximum Flow Problem 8.3: Edith Cohen: Shortest-Path Algorithms 8.4: S. Thomas McCormick: Minimum-Cost Single-Commodity Flow 8.5: Pierre Chardaire and Abdel Lisser: Minimum-Cost Multicommodity Flow 8.6: Ravindra K. Ahuja, Thomas L. Magnanti, and James B. Orlin: Minimum Spanning Tree Problem 9: Integer Programming 9.1: Nelson Maculan: Introduction 9.2: Nelson Maculan: Linear 0-1 Programming 9.3: Yves Crama and peter L. Hammer: Psedo-Boolean Optimization 9.4: Christodoulos A. Floudas: Mixed-Integer Nonlinear Optimization 9.5: Monique Guignard: Lagrangian Relaxation 9.6: Arne Lookketangen: Heuristics for 0-1 Mixed-Integer Programming 10: Theodore B. Trafalis and Suat Kasap: Artificial Neural Networks in Optimization and Applications 11: John R. Birge: Stochastic Programming 12: Hoang Tuy: Hierarchical Optimization 13: Michael C. Ferris and Christian Kanzow: Complementarity and Related Problems 14: Jose H. Dula: Data Envelopment Analysis 15: Yair Censor and Stavros A. Zenios: Parallel Algorithms in Optimization 16: Sanguthevar Rajasekaran: Randomization in Discrete Optimization: Annealing Algorithms Part Two: Applications 17: Problem Types 17.1: Chung-Yee Lee and Michael Pinedo: Optimization and Heuristics of Scheduling 17.2: John E. Beasley, Abilio Lucena, and Marcus Poggi de Aragao: The Vehicle Routing Problem 17.3: Ding-Zhu Du: Network Designs: Approximations for Steiner Minimum Trees 17.4: Edward G. Coffman, Jr., Janos Csirik, and Gerhard J. Woeginger: Approximate Solutions to Bin Packing Problems 17.5: Rainer E. Burkard: The Traveling Salesmand Problem 17.6: Dukwon Kim and Boghos D. Sivazlian: Inventory Management 17.7: Zvi Drezner: Location 17.8: Jun Gu, Paul W. Purdom, John Franco, and Benjamin W. Wah: Algorithms for the Satisfiability (SAT) Problem 17.9: Eranda Cela: Assignment Problems 18: Application Areas 18.1: Warren B. Powell: Transportation and Logistics 18.2: Gang Yu and Benjamin G. Thengvall: Airline Optimization 18.3: Alexandra M. Newman, Linda K. Nozick, and Candace Arai Yano: Optimization in the Rail Industry 18.4: Andres Weintraub Pohorille and John Hof: Forstry Industry 18.5: Stephen C. Graves: Manufacturing Planning and Control 18.6: Robert C. Leachman: Semiconductor Production Planning 18.7: Matthew E. Berge, John T. Betts, Sharon K. Filipowski, William P. Huffman, and David P. Young: Optimization in the Aerospace Industry 18.8: Energy 18.8.1: Gerson Couto de Oliveira, Sergio Granville, and Mario Pereira: Optimization in Electrical Power Systems 18.8.2: Roland N. Horne: Optimization Applications in Oil and Gas Recovery 18.8.3: Roger Z. Rios-Mercado: Natural Gas Pipeline Optimization 18.9: G. Anandalingam: Opimization of Telecommunications Networks 18.10: Stanislav Uryasev: Optimization of Test Intervals in Nuclear Engineering 18.11: Hussein A. Y. Etawil and Anthony Vannelli: Optimization in VLSI Design: Target Distance Models for Cell Placement 18.12: Michael Florian and Donald W. Hearn: Optimization Models in Transportation Planning 18.13: Guoliang Xue: Optimization in computation Molecular Biology 18.14: Anna Nagurney: Optimization in the Financial Services Industry 18.15: J. B. Rosen, John H. Glick, and E. Michael Gertz: Applied Large-Scale Nonlinear Optimization for Optimal Control of Partial Differential Equations and Differential Algebraic Equations 18.16: Kumaraswamy Ponnambalam: Optimization in Water Reservoir Systems 18.17: Ivan Dimov and Zahari Zlatev: Optimization Problems in Air-Pollution Modeling 18.18: Charles B. Moss: Applied Optimization in Agriculture 18.19: Petra Mutzel: Optimization in Graph Drawing 18.20: G. E. Stavroulakis: Optimization for Modeling of Nonlinear Interactions in Mechanics Part Three: Software 19: Emmanuel Fragniere and Jacek Gondzio: Optimization Modeling Languages 20: Stephen J. Wright: Optimization Software Packages 21: Andreas Fink, Stefan VoB, and David L. Woodruff: Optimization Software Libraries 22: John E. Beasley: Optimization Test Problem Libraries 23: Simone de L. Martins, Celso C. Ribeiro, and Noemi Rodriguez: Parallel Computing Environment 24: Catherine C. McGeoch: Experimental Analysis of Optimization Algorithms 25: Andreas Fink, Stefan VoB, and David L. Woodruff: Object-Oriented Programming 26: Michael A. Trick: Optimization and the Internet Directory of Contributors Index

631 citations


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