Statistical performance of subgradient step-size update rules in Lagrangian relaxations of chance-constrained optimization models
Statistical performance of subgradient step-size update rules in Lagrangian relaxations of chance-constrained optimization models
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.
Chance constraints, Lagrangian decomposition, Progressive hedging, Statistical guarantees, Subgradient
357-373
Ritter, Charlotte
e2d21b30-f6ca-464f-a77f-d4159fd04709
Singh, Bismark
9d3fc6cb-f55e-4562-9d5f-42f9a3ddd9a1
2023
Ritter, Charlotte
e2d21b30-f6ca-464f-a77f-d4159fd04709
Singh, Bismark
9d3fc6cb-f55e-4562-9d5f-42f9a3ddd9a1
Ritter, Charlotte and Singh, Bismark
(2023)
Statistical performance of subgradient step-size update rules in Lagrangian relaxations of chance-constrained optimization models.
Olenev, Nicholas, Evtushenko, Yuri, Malkova, Vlasta, Jaćimović, Milojica and Khachay, Michael
(eds.)
In Optimization and Applications - 14th International Conference, OPTIMA 2023, Revised Selected Papers: 14th International Conference, OPTIMA 2023, Petrovac, Montenegro, September 18–22, 2023, Revised Selected Papers.
vol. 14395 LNCS,
Springer Cham.
.
(doi:10.1007/978-3-031-47859-8_26).
Record type:
Conference or Workshop Item
(Paper)
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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e-pub ahead of print date: 10 November 2023
Published date: 2023
Additional Information:
Funding Information:
We gratefully acknowledge the compute resources and support provided by the Erlangen Regional Computing Center (RRZE). The authors acknowledge the financial support by the Federal Ministry for Economic Affairs and Energy of Germany in the project METIS (project number 03ET4064).
Publisher Copyright:
© 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.
Venue - Dates:
XIV International Conference Optimization and Applications (OPTIMA-2023), , Petrovac, Montenegro, 2023-09-18 - 2023-09-22
Keywords:
Chance constraints, Lagrangian decomposition, Progressive hedging, Statistical guarantees, Subgradient
Identifiers
Local EPrints ID: 484285
URI: http://eprints.soton.ac.uk/id/eprint/484285
ISSN: 0302-9743
PURE UUID: 7049c8af-fe81-4984-a8ad-8923d3c4e837
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Date deposited: 13 Nov 2023 18:57
Last modified: 18 Mar 2024 04:08
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Contributors
Author:
Charlotte Ritter
Author:
Bismark Singh
Editor:
Nicholas Olenev
Editor:
Yuri Evtushenko
Editor:
Vlasta Malkova
Editor:
Milojica Jaćimović
Editor:
Michael Khachay
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