On parallelizing dual decomposition in stochastic integer programming

Lubin, Miles; Martin, Richard R.; Petra, Cosmin G.; Sandikçi, Burhaneddi̇n

doi:10.1016/j.orl.2013.02.003

Cited by 54 publications

(38 citation statements)

References 16 publications

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“…Under such conditions, the best bound obtained from the Lagrangian dual can be obtained by solving the linear program (20). There are several methods for solving the dual problem (19), including subgradient methods [35], cutting plane, and bundle-type methods [16].…”

Section: Lower Bound Convergencementioning

confidence: 99%

“…There are several methods for solving the dual problem (19), including subgradient methods [35], cutting plane, and bundle-type methods [16]. The Dantzig-Wolfe column generation method [8] is an approach to solve the primal linear program (20). In [20], the authors show the duality between a cutting plane model of F (λ) and the primal linear program (20), and provide a method to recover a primal solution to (20) by solving the dual problem in the context of stochastic mixed integer programs.…”

Section: Lower Bound Convergencementioning

confidence: 99%

“…The Dantzig-Wolfe column generation method [8] is an approach to solve the primal linear program (20). In [20], the authors show the duality between a cutting plane model of F (λ) and the primal linear program (20), and provide a method to recover a primal solution to (20) by solving the dual problem in the context of stochastic mixed integer programs. They also suggest warm-starting the branch-and-price method using the bound and primal solution obtained using this implementation of the proximal bundle method.…”

Section: Lower Bound Convergencementioning

confidence: 99%

“…Because we are dealing with SMIPs, there is typically a duality gap between (20) and (12)- (17). The duality gap can be closed by branch-and-bound algorithms, where the bounding can be done by either solving the dual problem (19) or the primal problem (20).…”

Section: Lower Bound Convergencementioning

confidence: 99%

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Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs

et al. 2016

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We present a method for computing lower bounds in the progressive hedging algorithm (PHA) for two-stage and multi-stage stochastic mixed-integer programs. Computing lower bounds in the PHA allows one to assess the quality of the solutions generated by the algorithm contemporaneously. The lower bounds can be computed in any iteration of the algorithm by using dual prices that are calculated during execution of the standard PHA. We report computational results on stochastic unit commitment and stochastic server location problem instances, and explore the relationship between key PHA parameters and the quality of the resulting lower bounds. Abstract We present a method for computing lower bounds in the Progressive Hedging Algorithm (PHA) for two-stage and multi-stage stochastic mixedinteger programs. Computing lower bounds in the PHA allows one to assess the quality of the solutions generated by the algorithm contemporaneously. The lower bounds can be computed in any iteration of the algorithm by using dual prices that are calculated during execution of the standard PHA. We report computational results on stochastic unit commitment and stochastic server location problem instances, and explore the relationship between key PHA parameters and the quality of the resulting lower bounds.

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Section: Lower Bound Convergencementioning

confidence: 99%

Section: Lower Bound Convergencementioning

confidence: 99%

Section: Lower Bound Convergencementioning

confidence: 99%

Section: Lower Bound Convergencementioning

confidence: 99%

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Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs

et al. 2016

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“…Carøe and Schultz [3] developed a dual decomposition (DD) algorithm based on scenario decomposition and Lagrangian relaxation. Lubin et al [14] demonstrated the potential for parallel speedup by addressing the bottleneck of parallelizing dual decomposition. Originally proposed by Rockafellar and Wets [19] for stochastic programs with only continuous variables, progressive hedging (PH) has been successfully applied by Listes and Dekker [17], Fan and Liu [6], Watson and Woodruff [25], and many others as a heuristic to solve stochastic mixed-integer programs.…”

Section: Introductionmentioning

confidence: 99%

Integration of progressive hedging and dual decomposition in stochastic integer programs

Guo

Hackebeil

Ryan

et al. 2015

Operations Research Letters

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We present a method for integrating the Progressive Hedging (PH) algorithm and the Dual Decomposition (DD) algorithm of Carøe and Schultz for stochastic mixed-integer programs. Based on the correspondence between lower bounds obtained with PH and DD, a method to transform weights from PH to Lagrange multipliers in DD is found. Fast progress in early iterations of PH speeds up convergence of DD to an exact solution. We report computational results on server location and unit commitment instances. KeywordsStochastic programming, Mixed-integer programming, Progressive hedging, Dual decomposition, Lower bounding Disciplines Industrial Engineering | Systems EngineeringComments NOTICE: this is the author's version of a work that was accepted for publication in Operation Research Letters. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Operations Research Letters, [v.43, iss.3,(2015) AbstractWe present a method for integrating the Progressive Hedging (PH) algorithm and the Dual Decomposition (DD) algorithm of Carøe and Schultz for stochastic mixed-integer programs. Based on the correspondence between lower bounds obtained with PH and DD, a method to transform weights from PH to Lagrange multipliers in DD is found. Fast progress in early iterations of PH speeds up convergence of DD to an exact solution. We report computational results on server location and unit commitment instances.

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An Embarrassingly Parallel Method for Large-Scale Stochastic Programs

Sandikçi

Özaltın

2019

Springer Optimization and Its Applications

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On parallelizing dual decomposition in stochastic integer programming

Cited by 54 publications

References 16 publications

Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs

Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs

Integration of progressive hedging and dual decomposition in stochastic integer programs

An Embarrassingly Parallel Method for Large-Scale Stochastic Programs

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