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A unified framework for multistage mixed integer linear optimization

A unified framework for multistage mixed integer linear optimization
A unified framework for multistage mixed integer linear optimization

We introduce a unified framework for the study of multilevel mixed integer linear optimization problems and multistage stochastic mixed integer linear optimization problems with recourse. The framework highlights the common mathematical structure of the two problems and allows for the development of a common algorithmic framework. Focusing on the two-stage case, we investigate, in particular, the nature of the value function of the second-stage problem, highlighting its connection to dual functions and the theory of duality for mixed integer linear optimization problems, and summarize different reformulations. We then present two main solution techniques, one based on a Benders-like decomposition to approximate either the risk function or the value function, and the other one based on cutting plane generation.

Convexification-based methods, Decomposition methods, Discrete optimization, Multilevel optimization, Multistage stochastic optimization, Primal and dual functions
1931-6828
513-560
Springer
Bolusani, Suresh
52482499-0d3d-48ea-8ffb-d6a875a221af
Coniglio, Stefano
03838248-2ce4-4dbc-a6f4-e010d6fdac67
Ralphs, Ted K.
f5b9910a-4bf6-4b1b-b685-3ae68a3125fd
Tahernejad, Sahar
f1fe4295-dab8-47b1-a5cb-bf46aa0829f2
Bolusani, Suresh
52482499-0d3d-48ea-8ffb-d6a875a221af
Coniglio, Stefano
03838248-2ce4-4dbc-a6f4-e010d6fdac67
Ralphs, Ted K.
f5b9910a-4bf6-4b1b-b685-3ae68a3125fd
Tahernejad, Sahar
f1fe4295-dab8-47b1-a5cb-bf46aa0829f2

Bolusani, Suresh, Coniglio, Stefano, Ralphs, Ted K. and Tahernejad, Sahar (2020) A unified framework for multistage mixed integer linear optimization. In, Springer Optimization and Its Applications. (HASH(0xb9eb228), 161) Springer, pp. 513-560. (doi:10.1007/978-3-030-52119-6_18).

Record type: Book Section

Abstract

We introduce a unified framework for the study of multilevel mixed integer linear optimization problems and multistage stochastic mixed integer linear optimization problems with recourse. The framework highlights the common mathematical structure of the two problems and allows for the development of a common algorithmic framework. Focusing on the two-stage case, we investigate, in particular, the nature of the value function of the second-stage problem, highlighting its connection to dual functions and the theory of duality for mixed integer linear optimization problems, and summarize different reformulations. We then present two main solution techniques, one based on a Benders-like decomposition to approximate either the risk function or the value function, and the other one based on cutting plane generation.

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More information

Published date: 24 November 2020
Additional Information: Publisher Copyright: © 2020, Springer Nature Switzerland AG. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.
Keywords: Convexification-based methods, Decomposition methods, Discrete optimization, Multilevel optimization, Multistage stochastic optimization, Primal and dual functions

Identifiers

Local EPrints ID: 448745
URI: http://eprints.soton.ac.uk/id/eprint/448745
ISSN: 1931-6828
PURE UUID: 3994a233-7daa-4ada-9b67-65db7391e63a
ORCID for Stefano Coniglio: ORCID iD orcid.org/0000-0001-9568-4385

Catalogue record

Date deposited: 04 May 2021 16:50
Last modified: 28 Apr 2022 02:14

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Contributors

Author: Suresh Bolusani
Author: Ted K. Ralphs
Author: Sahar Tahernejad

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