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

Journal Article · · Mathematical Programming
 [1];  [2];  [3];  [4];  [5];  [5]
  1. Sabre Holdings, Southlake, TX (United States)
  2. Texas A & M Univ., College Station, TX (United States)
  3. Iowa State Univ., Ames, IA (United States)
  4. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  5. Univ. of California, Davis, CA (United States)
+ Show Author Affiliations
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. In conclusion, 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.
Research Organization:
Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
AC04-94AL85000
OSTI ID:
1310314
Report Number(s):
SAND--2013-9195J; PII: 1000
Journal Information:
Mathematical Programming, Journal Name: Mathematical Programming Journal Issue: 1 Vol. 157; ISSN 0025-5610
Publisher:
SpringerCopyright Statement
Country of Publication:
United States
Language:
English

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Cited By (7)

Stochastic dual dynamic integer programming journal March 2018
A Progressive Hedging based branch-and-bound algorithm for mixed-integer stochastic programs journal June 2018
Progressive hedging for stochastic programs with cross-scenario inequality constraints journal November 2019
A finite $$\epsilon $$-convergence algorithm for two-stage stochastic convex nonlinear programs with mixed-binary first and second-stage variables journal August 2019
Optimising data-driven network under limited resource: a partial diversification approach journal August 2018
Combining penalty-based and Gauss-Seidel methods for solving stochastic mixed-integer problems journal March 2018
Modeling and Solution Techniques Used for Hydro Generation Scheduling journal July 2019

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Related Subjects

97 MATHEMATICS AND COMPUTING
decomposition algorithms
lower bounding
stochastic mixed-integer programming