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Approximating Two-Stage Chance-Constrained Programs with Classical Probability Bounds

Journal Article · · Optimization Letters
 [1];  [2]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Discrete Math & Optimization
  2. Sandia National Lab. (SNL-CA), Livermore, CA (United States). Data Science & Cyber Analytics
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We consider a joint-chance constraint (JCC) as a union of sets, and approximate this union using bounds from classical probability theory. When these bounds are used in an optimization model constrained by the JCC, we obtain corresponding upper and lower bounds on the optimal objective function value. We compare the strength of these bounds against each other under two different sampling schemes, and observe that a larger correlation between the uncertainties tends to result in more computationally challenging optimization models. We also observe the same set of inequalities to provide the tightest upper and lower bounds in our computational experiments.

Research Organization:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
AC04-94AL85000
OSTI ID:
1492794
Report Number(s):
SAND-2019-0432J; 671570
Journal Information:
Optimization Letters, Journal Name: Optimization Letters; ISSN 1862-4472
Publisher:
Springer NatureCopyright Statement
Country of Publication:
United States
Language:
English

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