Solving joint chance constrained problems using regularization and Benders’ decomposition

Lukáš Adam (), Martin Branda, Holger Heitsch and René Henrion
Additional contact information
Lukáš Adam: Southern University of Science and Technology
Martin Branda: The Czech Academy of Sciences, Institute of Information Theory and Automation
Holger Heitsch: Weierstrass Institute for Applied Analysis and Stochastics
René Henrion: Weierstrass Institute for Applied Analysis and Stochastics

Annals of Operations Research, 2020, vol. 292, issue 2, No 6, 683-709

Abstract: Abstract We consider stochastic programs with joint chance constraints with discrete random distribution. We reformulate the problem by adding auxiliary variables. Since the resulting problem has a non-regular feasible set, we regularize it by increasing the feasible set. We solve the regularized problem by iteratively solving a master problem while adding Benders’ cuts from a slave problem. Since the number of variables of the slave problem equals to the number of scenarios, we express its solution in a closed form. We show convergence properties of the solutions. On a gas network design problem, we perform a numerical study by increasing the number of scenarios and compare our solution with a solution obtained by solving the same problem with the continuous distribution.

Keywords: Stochastic programming; Chance constrained programming; Optimality conditions; Regularization; Benders’ decomposition; Gas networks; 90C15; 90C26; 49M05 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1007/s10479-018-3091-9 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:annopr:v:292:y:2020:i:2:d:10.1007_s10479-018-3091-9

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/10479

DOI: 10.1007/s10479-018-3091-9

Access Statistics for this article

Annals of Operations Research is currently edited by Endre Boros

More articles in Annals of Operations Research from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().