Two-stage robust mixed integer programming problem with objective uncertainty
Many real problems with uncertain parameters can be modeled as two-stage robust mixed integer programming problems (RMIPs). Due to the complex nature of this kind of problems, this paper focuses on the two-stage RMIPs with objective uncertainty. Based on the results that the augmented Lagrangian is...
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| Published in: | Optimization letters Vol. 12; no. 5; pp. 959 - 969 |
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| Format: | Journal Article |
| Language: | English |
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Springer Berlin Heidelberg
01.07.2018
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| ISSN: | 1862-4472, 1862-4480 |
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| Abstract | Many real problems with uncertain parameters can be modeled as two-stage robust mixed integer programming problems (RMIPs). Due to the complex nature of this kind of problems, this paper focuses on the two-stage RMIPs with objective uncertainty. Based on the results that the augmented Lagrangian is a strong dual for integer programming Boland and Eberhard (Math Program 150(2):491–509,
2015
), we present the upper and lower bounds. In a special case, we show that the two-stage RMIPs can be equivalently reformulated as a solvable minimax problem. |
|---|---|
| AbstractList | Many real problems with uncertain parameters can be modeled as two-stage robust mixed integer programming problems (RMIPs). Due to the complex nature of this kind of problems, this paper focuses on the two-stage RMIPs with objective uncertainty. Based on the results that the augmented Lagrangian is a strong dual for integer programming Boland and Eberhard (Math Program 150(2):491–509,
2015
), we present the upper and lower bounds. In a special case, we show that the two-stage RMIPs can be equivalently reformulated as a solvable minimax problem. |
| Author | Zhang, Ning |
| Author_xml | – sequence: 1 givenname: Ning orcidid: 0000-0001-5487-6524 surname: Zhang fullname: Zhang, Ning email: ningzhang_2008@yeah.net organization: Department of Mathematics, National University of Singapore, Future Resilient Systems, Singapore ETH Centre |
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| Cites_doi | 10.1016/0012-365X(79)90147-X 10.1007/BF01585518 10.1007/BF01386316 10.1007/s10107-014-0818-5 10.1007/s10107-016-1012-8 10.1287/opre.2013.1172 10.1287/opre.2015.1365 10.1007/s10107-003-0454-y 10.1287/moor.1100.0444 10.1287/opre.2015.1392 10.1515/9781400873173 10.1515/9781400831050 10.1137/1016053 10.1016/0012-365X(77)90028-0 10.1287/moor.1090.0440 10.1007/BF01583794 10.1287/opre.1080.0605 10.1007/s10107-014-0763-3 10.1287/ijoc.2016.0696 10.1109/CDC.2011.6161382 |
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| Keywords | Mixed integer programming Objective uncertainty Two-stage robust optimization Augmented Lagrangian |
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| Title | Two-stage robust mixed integer programming problem with objective uncertainty |
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