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

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.
Authors:
 [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)
Publication Date:
OSTI Identifier:
1310314
Report Number(s):
SAND--2013-9195J
Journal ID: ISSN 0025-5610; PII: 1000
Grant/Contract Number:
AC04-94AL85000
Type:
Accepted Manuscript
Journal Name:
Mathematical Programming
Additional Journal Information:
Journal Volume: 157; Journal Issue: 1; Journal ID: ISSN 0025-5610
Publisher:
Springer
Research Org:
Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING stochastic mixed-integer programming; decomposition algorithms; lower bounding