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Nonanticipative duality, relaxations, and formulations for chance-constrained stochastic programs

Shabbir Ahmed, James Luedtke, Yongjia Song, Weijun Xie
2016 Mathematical programming  
We propose two new Lagrangian dual problems for chance-con-strained stochastic programs based on relaxing nonanticipativity constraints.  ...  We also derive two new primal MIP formulations and demonstrate that for chanceconstrained linear programs, the continuous relaxations of these formulations yield bounds equal to the proposed dual bounds  ...  for chance-constrained linear programs, or a lower bound on them for chance-constrained mixed integer programs.  ... 
doi:10.1007/s10107-016-1029-z fatcat:2dl4lqfderhfnnfgi5mf2czsma

Probability Objectives in Stochastic Programs with Recourse [chapter]

Rüdiger Schultz
2003 IFIP Advances in Information and Communication Technology  
For the two-stage case, we analyse structural properties and propose algorithms both for models with integer decisions and for those without .  ...  Traditional models in multistage stochastic programming are directed to minimizing the expected value of random optimal costs arising in a multistage, non-anticipative decision process under uncertainty  ...  I am grateful to Morten Riis (University of Aarhus), Werner Romisch (Humboldt-University Berlin), and Stephan Tiedemann (Gerhard-Mercator University Duisburg) for stimulating discussions and fruitful cooperation  ... 
doi:10.1007/978-0-387-35699-0_8 fatcat:ki33nabvovd37b7dqmwmcz7aiq

Stochastic programming approaches to stochastic scheduling

John R. Birge, M. A. H. Dempstert
1996 Journal of Global Optimization  
Yields, resource availability, performance, demand, costs, and revenues may all *  ...  which uses large deviations theory to produce, from the original chance- constrained stochastic programming formulation.  ...  The chance-constrained stochastic programming problem (g)-(12) mth Poisson jlows and ran- dom call muting has an approximate deterministic equivalent linear progmmmzng problem gwen by (13)-(16)  ... 
doi:10.1007/bf00121682 fatcat:2otwqvp7iff6tc4tcw7cfvmkym

Fundamentals and recent developments in stochastic unit commitment

Martin Håberg
2019 International Journal of Electrical Power & Energy Systems  
Focusing primarily on scenario-based approaches, this article summarizes the fundamental concepts of stochastic unit commitment, including the representation of uncertainty, different problem formulations  ...  and the most common decomposition techniques applied to solve the problem.  ...  Acknowledgements The author wishes to thank Gerard Doorman at Statnett for valuable feedback and support.  ... 
doi:10.1016/j.ijepes.2019.01.037 fatcat:dbq7xl27jne6fkitg576ke34tu

Recent advances in mathematical programming techniques for the optimization of process systems under uncertainty

Ignacio E. Grossmann, Robert M. Apap, Bruno A. Calfa, Pablo García-Herreros, Qi Zhang
2016 Computers and Chemical Engineering  
hedging against uncertainty (robust/chance constrained optimization vs. stochastic programming), large computational expense (often orders of magnitude larger than deterministic models), and difficulty  ...  Optimization under uncertainty has been an active area of research for many years.  ...  The authors would like to acknowledge financial support from NSF Grant No. 1159443, Praxair, The Dow Chemical Company, the ExxonMobil Upstream Research Company, and the Center for Advanced Process Decision-making  ... 
doi:10.1016/j.compchemeng.2016.03.002 fatcat:kbdi23aghbh25dnd455t7atcdm

Parallel Scenario Decomposition of Risk-Averse 0-1 Stochastic Programs

Yan Deng, Shabbir Ahmed, Siqian Shen
2018 INFORMS journal on computing  
Ahmed et al. (2015b) generalize the scenario decomposition approach for chance-constrained binary programs and derive the Lagrangian dual problems based on relaxing nonanticipativity constraints.  ...  Watson et al. (2010) generalize the approach to solving chanceconstrained programs, where they relax both the nonanticipativity constraints and the knapsack constraint for reformulating a chance constraint  ...  Yan Deng is also grateful for the support from Michigan Institute for Computational Discovery and Engineering Fellowship.  ... 
doi:10.1287/ijoc.2017.0767 fatcat:vu7isy5iizebfpy5nsap5taqiy

Lagrangian Dual Decision Rules for Multistage Stochastic Mixed Integer Programming [article]

Maryam Daryalal, Merve Bodur, James R. Luedtke
2022 arXiv   pre-print
Multistage stochastic programs can be approximated by restricting policies to follow decision rules.  ...  In this work, we introduce Lagrangian dual decision rules (LDDRs) for multistage stochastic mixed-integer programming (MSMIP) which overcome this difficulty by applying decision rules in a Lagrangian dual  ...  Brown et al. (2010) study information relaxation for stochastic dynamic programs and, similar to our approach, penalize the violation of nonanticipativity constraints (i.e., the ones that ensure consistency  ... 
arXiv:2001.00761v2 fatcat:naaqrkrxxnhtrjerhcc4movgjy

Risk-Averse Optimization for Resilience Enhancement of Complex Engineering Systems under Uncertainties [article]

Jiaxin Wu, Pingfeng Wang
2020 arXiv   pre-print
Case study results based on the IEEE 37-bus test feeder demonstrate the benefits of using the proposed framework for resilience improvement as well as the advantages of adopting SO formulations.  ...  Moreover, different from conventional SO using deterministic equivalent formulations, additional risk measure is implemented for this study because of the temporal sparsity of the decision making in applications  ...  In order to tackle the challenges imposed by uncertainties in decision making process, techniques such as chance constrained optimization, robust optimization (RO) and stochastic optimization (SO) with  ... 
arXiv:2009.02351v1 fatcat:yuypceokobgnjmfwn7tsiamrvi

Consensus Distributionally Robust Optimization with Phi-Divergence

Shunichi Ohmori
2021 IEEE Access  
We applied the proposed method to linear programming, quadratic programming, and second-order cone programming in numerical experiments and verified its effectiveness.  ...  In traditional stochastic programming, a decision is sought that minimizes the expected cost over the probability distribution of the unknown parameters.  ...  Nemirovski [20] presented several simulation-based and simulation-free computationally tractable approximations of chance-constrained convex programs, primarily those of chance-constrained linear, conic  ... 
doi:10.1109/access.2021.3091432 fatcat:cuujkl6mjbcglcw4ofoibwvtsu

On Risk-Averse Stochastic Semidefinite Programs with Continuous Recourse [article]

Matthias Claus, Rüdiger Schultz, Kai Spürkel, Tobias Wollenberg
2018 arXiv   pre-print
In this paper, we introduce mean-risk models for stochastic SDPs and study structural properties as convexity and (Lipschitz) continuity.  ...  We discuss extended formulations for stochastic SDPs under finite discrete distributions, which turn out to be deterministic (mixed-integer) SDPs that are (almost) block-structured for many popular risk  ...  Chance constrained SDP models have been introduced by Ariyawansa and Zhu in [26, Chapter 3] , where an application to the stochastic minimum-volume covering ellipsoid problem is considered.  ... 
arXiv:1812.09879v1 fatcat:ikxjdvy5vjf4jjjytdjn73ntf4

Tutorials on Advanced Optimization Methods [article]

Wei Wei
2020 arXiv   pre-print
This material is a good reference for self-learners who have basic knowledge in linear algebra and linear programming.  ...  programming, robust optimization, and equilibrium/game problems.  ...  C.4.1 Robust Chance Constrained Stochastic Program We introduce robust chance-constrained stochastic programs with distributional robustness.  ... 
arXiv:2007.13545v1 fatcat:o5rx62tjzvfunitksen4dlci6m

A Review of Stochastic Programming Methods for Optimization of Process Systems Under Uncertainty

Can Li, Ignacio E. Grossmann
2021 Frontiers in Chemical Engineering  
The mathematical formulations and algorithms for two-stage and multistage stochastic programming are reviewed with illustrative examples from process industries.  ...  stochastic programming.  ...  TABLE 2 | 2 Summary of stochastic programming, chance-constrained programming, and robust optimization.  ... 
doi:10.3389/fceng.2020.622241 fatcat:32gnbbfemrh6hlbrcorxvnrksa

Primal and dual linear decision rules in stochastic and robust optimization

Daniel Kuhn, Wolfram Wiesemann, Angelos Georghiou
2009 Mathematical programming  
Linear stochastic programming provides a flexible toolbox for analyzing reallife decision situations, but it can become computationally cumbersome when recourse decisions are involved.  ...  Our method remains applicable if the stochastic program has random recourse and multiple decision stages. It also extends to cases involving ambiguous probability distributions.  ...  Their potential for complexity reduction in multistage stochastic programming has first been highlighted by Shapiro and Nemirovski [26] , and their suitability for solving chance-constrained stochastic  ... 
doi:10.1007/s10107-009-0331-4 fatcat:not4cmdsz5h65h6cpj2xybqjo4

A Linear Decision-Based Approximation Approach to Stochastic Programming

Xin Chen, Melvyn Sim, Peng Sun, Jiawei Zhang
2008 Operations Research  
A different approach is suggested by Chen, Sim and Sun [17] for chance-constrained stochastic programs, which assumes only limited distributional information such as known mean, support, and some deviation  ...  This new class of decisions rules is suitable for stochastic optimization problems with semi-complete recourse variables, a relaxation of complete recourse.  ...  Acknowledgment: We thank the AE and the referees for many useful comments on previous versions of the paper.  ... 
doi:10.1287/opre.1070.0457 fatcat:ugpuyvwlujesfjhwxcgn66hpja

Computational strategies for non-convex multistage MINLP models with decision-dependent uncertainty and gradual uncertainty resolution

Bora Tarhan, Ignacio E. Grossmann, Vikas Goel
2011 Annals of Operations Research  
In order to account for the decision-dependent uncertainties and gradual uncertainty resolution, we propose a multistage stochastic programming model in which the non-anticipativity constraints in the  ...  In this paper, we address a generic non-convex MINLP model for such planning problems where the uncertain parameters are assumed to follow discrete distributions and the decisions are made on a discrete  ...  Introduction to Stochastic Programming. Springer-Verlag, New York.  ... 
doi:10.1007/s10479-011-0855-x fatcat:gbi72adkt5chbgu4szvjy7pzfm
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