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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 proposes a new approach to analyze stochastic systems based on robust optimization, which replaces the Kolmogorov axioms and the concept of random variables as primitives of probability theory with uncertainty sets that are derived from some of the asymptotic implications of probabilities theory like the central limit theorem.
Abstract: Modern probability theory, whose foundation is based on the axioms set forth by Kolmogorov, is currently the major tool for performance analysis in stochastic systems. While it offers insights in understanding such systems, probability theory, in contrast to optimization, has not been developed with computational tractability as an objective when the dimension increases. Correspondingly, some of its major areas of application remain unsolved when the underlying systems become multidimensional: Queueing networks, auction design in multi-item, multi-bidder auctions, network information theory, pricing multi-dimensional options, among others. We propose a new approach to analyze stochastic systems based on robust optimization. The key idea is to replace the Kolmogorov axioms and the concept of random variables as primitives of probability theory, with uncertainty sets that are derived from some of the asymptotic implications of probability theory like the central limit theorem. In addition, we observe that several desired system properties such as incentive compatibility and individual rationality in auction design are naturally expressed in the language of robust optimization. In this way, the performance analysis questions become highly structured optimization problems (linear, semidefinite, mixed integer) for which there exist efficient, practical algorithms that are capable of solving problems in high dimensions. We demonstrate that the proposed approach achieves computationally tractable methods for (a) analyzing queueing networks, (b) designing multi-item, multi-bidder auctions with budget constraints, and (c) pricing multi-dimensional options.

157 citations

Journal ArticleDOI
TL;DR: A model is proposed in which periodic optimal portfolio adjustments are determined with the objective of minimizing a cumulative risk measure over the investment horizon, while satisfying portfolio diversity constraints at each period and achieving or exceeding a desired terminal expected wealth target.

157 citations

Journal ArticleDOI
TL;DR: Methodology for sharing cuts in decomposition algorithms for stochastic programs that satisfy certain interstage dependency models enable sampling-based algorithms to handle a richer class of multistage problems, and may also be used to accelerate the convergence of exact decompose algorithms.
Abstract: Multistage stochastic programs with interstage independent random parameters have recourse functions that do not depend on the state of the system. Decomposition-based algorithms can exploit this structure by sharing cuts (outer-linearizations of the recourse function) among different scenario subproblems at the same stage. The ability to share cuts is necessary in practical implementations of algorithms that incorporate Monte Carlo sampling within the decomposition scheme. In this paper, we provide methodology for sharing cuts in decomposition algorithms for stochastic programs that satisfy certain interstage dependency models. These techniques enable sampling-based algorithms to handle a richer class of multistage problems, and may also be used to accelerate the convergence of exact decomposition algorithms.

156 citations

Journal ArticleDOI
01 Jan 2014-Energy
TL;DR: In this article, a two-stage stochastic programming model is proposed to schedule energy and reserve provided by both of generating units and responsive loads in power systems with high penetration of wind power.

156 citations

Journal ArticleDOI
TL;DR: Resource allocation issues are investigated in this paper for multiuser wireless transmissions based on orthogonal frequency division multiplexing (OFDM) using convex and stochastic optimization tools.
Abstract: Resource allocation issues are investigated in this paper for multiuser wireless transmissions based on orthogonal frequency division multiplexing (OFDM). Relying on convex and stochastic optimization tools, the novel approach to resource allocation includes: i) development of jointly optimal subcarrier, power, and rate allocation for weighted sum-average-rate maximization; ii) judicious formulation and derivation of the optimal resource allocation for maximizing the utility of average user rates; and iii) development of the stochastic resource allocation schemes, and rigorous proof of their convergence and optimality. Simulations are also provided to demonstrate the merits of the novel schemes.

156 citations


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