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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: This work proves the almost-sure convergence of a class of sampling-based nested decomposition algorithms for multistage stochastic convex programs in which the stage costs are general convex functions of the decisions and uncertainty is modelled by a scenario tree.
Abstract: We prove the almost-sure convergence of a class of sampling-based nested decomposition algorithms for multistage stochastic convex programs in which the stage costs are general convex functions of the decisions and uncertainty is modelled by a scenario tree. As special cases, our results imply the almost-sure convergence of stochastic dual dynamic programming, cutting-plane and partial-sampling CUPPS algorithm, and dynamic outer-approximation sampling algorithms when applied to problems with general convex cost functions.

115 citations

Book ChapterDOI
01 Jan 2008
TL;DR: This chapter surveys existing techniques for such combinations of mathematical programming methods and metaheuristics and classifies them into ten methodological categories.
Abstract: Summary. Several different ways exist for approaching hard optimization problems. Mathematical programming techniques, including (integer) linear programming based methods, and metaheuristic approaches are two highly successful streams for combinatorial problems. These two have been established by different communities more or less in isolation from each other. Only over the last years a larger number of researchers recognized the advantages and huge potentials of building hybrids of mathematical programming methods and metaheuristics. In fact, many problems can be practically solved much better by exploiting synergies between these different approaches than by “pure” traditional algorithms. The crucial issue is how mathematical programming methods and metaheuristics should be combined for achieving those benefits. Many approaches have been proposed in the last few years. After giving a brief introduction to the basics of integer linear programming, this chapter surveys existing techniques for such combinations and classifies them into ten methodological categories.

115 citations

Journal ArticleDOI
Alan J. King1
TL;DR: It is found that arbitrage pricing in incomplete markets fails to model incentives to buy or sell options, and an extension of the model to incorporate pre-existing liabilities and endowments reveals the reasons why buyers and sellers trade in options.
Abstract: The hedging of contingent claims in the discrete time, discrete state case is analyzed from the perspective of modeling the hedging problem as a stochastic program. Application of conjugate duality leads to the arbitrage pricing theorems of financial mathematics, namely the equivalence of absence of arbitrage and the existence of a probability measure that makes the price process into a martingale. The model easily extends to the analysis of options pricing when modeling risk management concerns and the impact of spreads and margin requirements for writers of contingent claims. However, we find that arbitrage pricing in incomplete markets fails to model incentives to buy or sell options. An extension of the model to incorporate pre-existing liabilities and endowments reveals the reasons why buyers and sellers trade in options. The model also indicates the importance of financial equilibrium analysis for the understanding of options prices in incomplete markets.

115 citations

Journal ArticleDOI
TL;DR: The purpose of the paper is to present the numerical results of a comparative study of eleven mathematical programming codes which represent typical realizations of the mathematical methods mentioned in the structural optimization system MBB-LAGRANGE, which proceeds from a typical finite element analysis.
Abstract: For FE-based structural optimization systems, a large variety of different numerical algorithms is available, e.g. sequential linear programming, sequential quadratic programming, convex approximation, generalized reduced gradient, multiplier, penalty or optimality criteria methods, and combinations of these approaches. The purpose of the paper is to present the numerical results of a comparative study of eleven mathematical programming codes which represent typical realizations of the mathematical methods mentioned. They are implemented in the structural optimization system MBB-LAGRANGE, which proceeds from a typical finite element analysis. The comparative results are obtained from a collection of 79 test problems. The majority of them are academic test cases, the others possess some practicalreal life background. Optimization is performed with respect to sizing of trusses and beams, wall thicknesses, etc., subject to stress, displacement, and many other constraints. Numerical comparison is based on reliability and efficiency measured by calculation time and number of analyses needed to reach a certain accuracy level.

115 citations

Journal ArticleDOI
TL;DR: In this paper, the authors present a tool set robust to changes in demand that considers a set of possible, discrete demand scenarios with associated probabilities, and determines the tools to purchase, under a budget constraint, to minimize weighted average unmet demand.
Abstract: In the semiconductor industry, capacity planning, the calculation of number of tools needed to manufacture forecasted product demands, is difficult because of sensitivity to product mix and uncertainty in future demand. Planning for a single demand profile can result in a large gap between planned capacity and actual capability when the realized product mix turns out differently from the one planned. This paper presents a method which accepts this uncertainty and uses stochastic integer programming to find a tool set robust to changes in demand. It considers a set of possible, discrete demand scenarios with associated probabilities, and determines the tools to purchase, under a budget constraint, to minimize weighted average unmet demand. The resulting robust tool set deals well with all the scenarios at no or minimal additional cost compared to that for a single demand profile. We also discuss the modifications of conventional business processes, needed to implement this method for dealing explicitly with uncertainty in demand.

115 citations


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