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Saddle point approximation approaches for two-stage robust optimization problems

  • Ning Zhang
  • Chang FangEmail author
Article
  • 42 Downloads

Abstract

This paper aims to present improvable and computable approximation approaches for solving the two-stage robust optimization problem, which arises from various applications such as optimal energy management and production planning. Based on sampling finite number scenarios of uncertainty, we can obtain a lower bound approximation and show that the corresponding solution is at least \({\varepsilon }\)-level feasible. Moreover, piecewise linear decision rules (PLDRs) are also introduced to improve the upper bound that obtained by the widely-used linear decision rule. Furthermore, we show that both the lower bound and upper bound approximation problems can be reformulated into solvable saddle point problems and consequently be solved by the mirror descent method.

Keywords

Two-stage robust optimization Randomized approach Piecewise linear decision rule Saddle point problem Mirror descent algorithm 

Notes

Acknowledgements

We would like to thank Professor Xu Huan for his constructive suggestions on the idea of solving the two-stage robust optimization by using the randomized approach.

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Computer Science and TechnologyDongguan University of TechnologyDongguanChina
  2. 2.School of Economics and ManagementAnhui Normal UniversityWuhu CityChina

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