Statistical Performance of Subgradient Step-Size Update Rules in Lagrangian Relaxations of Chance-Constrained Optimization Models
Ritter C, Singh B (2023)
Publication Type: Conference contribution
Publication year: 2023
Journal
Publisher: Springer Science and Business Media Deutschland GmbH
Book Volume: 14395 LNCS
Pages Range: 357-373
Conference Proceedings Title: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Event location: Petrovac
ISBN: 9783031478581
DOI: 10.1007/978-3-031-47859-8_26
Abstract
Lagrangian relaxation schemes, coupled with a subgradient procedure, are frequently employed to solve chance-constrained optimization models. Subgradient procedures typically rely on step-size update rules. Although there is extensive research on the properties of these step-size update rules, there is little consensus on which rules are most suitable practically; especially, when the underlying model is a computationally challenging instance of a chance-constrained program. To close this gap, we seek to determine whether a single step-size rule can be statistically guaranteed to perform better than others. We couple the Lagrangian procedure with three strategies to identify lower bounds for two-stage chance-constrained programs. We consider two instances of such models that differ in the presence of binary variables in the second-stage. With a series of computational experiments, we demonstrate—in marked contrast to existing theoretical results—that no significant statistical differences in terms of optimality gaps is detected between six well-known step-size update rules. Despite this, our results demonstrate that a Lagrangian procedure provides computational benefit over a naive solution method—regardless of the underlying step-size update rule.
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United Kingdom (GB)How to cite
APA:
Ritter, C., & Singh, B. (2023). Statistical Performance of Subgradient Step-Size Update Rules in Lagrangian Relaxations of Chance-Constrained Optimization Models. In Nicholas Olenev, Yuri Evtushenko, Vlasta Malkova, Milojica Jaćimović, Michael Khachay (Eds.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 357-373). Petrovac, ME: Springer Science and Business Media Deutschland GmbH.
MLA:
Ritter, Charlotte, and Bismark Singh. "Statistical Performance of Subgradient Step-Size Update Rules in Lagrangian Relaxations of Chance-Constrained Optimization Models." Proceedings of the 14th International Conference on Optimization and Applications, OPTIMA 2023, Petrovac Ed. Nicholas Olenev, Yuri Evtushenko, Vlasta Malkova, Milojica Jaćimović, Michael Khachay, Springer Science and Business Media Deutschland GmbH, 2023. 357-373.
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