A Unified Framework for Multistage Mixed Integer Linear Optimization

Suresh Bolusani (), Stefano Coniglio (), Ted K. Ralphs () and Sahar Tahernejad ()
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Suresh Bolusani: Lehigh University
Stefano Coniglio: University of Southampton
Ted K. Ralphs: Lehigh University
Sahar Tahernejad: Lindo Systems, Inc.

Chapter Chapter 18 in Bilevel Optimization, 2020, pp 513-560 from Springer

Abstract: 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.

Keywords: Multilevel optimization; Multistage stochastic optimization; Discrete optimization; Primal and dual functions; Decomposition methods; Convexification-based methods (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-52119-6_18

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DOI: 10.1007/978-3-030-52119-6_18

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