An algorithm for two-stage stochastic mixed-integer nonlinear convex problems
We present an algorithm to solve two-stage stochastic convex problems, whose objective function and constraints are nonlinear. It is based on the twin-node-family concept involved in the Branch-and-Fix Coordination method. These problems have 0–1 mixed-integer recourse variables in the first stage a...
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| Published in: | Annals of operations research Vol. 235; no. 1; pp. 581 - 598 |
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| Main Author: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
New York
Springer US
01.12.2015
Springer Springer Nature B.V |
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| ISSN: | 0254-5330, 1572-9338 |
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| Abstract | We present an algorithm to solve two-stage stochastic convex problems, whose objective function and constraints are nonlinear. It is based on the twin-node-family concept involved in the Branch-and-Fix Coordination method. These problems have 0–1 mixed-integer recourse variables in the first stage and only continuous variables in the second stage. The non-anticipativity constraints are satisfied by means of the twin-node-family strategy. In this work to solve each nonlinear convex subproblem at each node we propose the solution of sequences of quadratic subproblems. Since the convexity of the constraints we can approximate them by means of outer approximations. These methods have been implemented in C
+
+
with the help of Cplex 12.1, which only solves the quadratic approximations. The test problems have been randomly generated by using a C
+
+
code developed by this author. Numerical experiments have been performed and its efficiency has been compared with that of well-known codes. |
|---|---|
| AbstractList | We present an algorithm to solve two-stage stochastic convex problems, whose objective function and constraints are nonlinear. It is based on the twin-node-family concept involved in the Branch-and-Fix Coordination method. These problems have 0-1 mixed-integer recourse variables in the first stage and only continuous variables in the second stage. The non-anticipativity constraints are satisfied by means of the twin-node-family strategy. In this work to solve each nonlinear convex subproblem at each node we propose the solution of sequences of quadratic subproblems. Since the convexity of the constraints we can approximate them by means of outer approximations. These methods have been implemented in C with the help of Cplex 12.1, which only solves the quadratic approximations. The test problems have been randomly generated by using a C code developed by this author. Numerical experiments have been performed and its efficiency has been compared with that of well-known codes. We present an algorithm to solve two-stage stochastic convex problems, whose objective function and constraints are nonlinear. It is based on the twin-node-family concept involved in the Branch-and-Fix Coordination method. These problems have 0–1 mixed-integer recourse variables in the first stage and only continuous variables in the second stage. The non-anticipativity constraints are satisfied by means of the twin-node-family strategy. In this work to solve each nonlinear convex subproblem at each node we propose the solution of sequences of quadratic subproblems. Since the convexity of the constraints we can approximate them by means of outer approximations. These methods have been implemented in C + + with the help of Cplex 12.1, which only solves the quadratic approximations. The test problems have been randomly generated by using a C + + code developed by this author. Numerical experiments have been performed and its efficiency has been compared with that of well-known codes. (ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image).We present an algorithm to solve two-stage stochastic convex problems, whose objective function and constraints are nonlinear. It is based on the twin-node-family concept involved in the Branch-and-Fix Coordination method. These problems have 0-1 mixed-integer recourse variables in the first stage and only continuous variables in the second stage. The non-anticipativity constraints are satisfied by means of the twin-node-family strategy. In this work to solve each nonlinear convex subproblem at each node we propose the solution of sequences of quadratic subproblems. Since the convexity of the constraints we can approximate them by means of outer approximations. These methods have been implemented in C... with the help of Cplex 12.1, which only solves the quadratic approximations. The test problems have been randomly generated by using a C... code developed by this author. Numerical experiments have been performed and its efficiency has been compared with that of well-known codes. |
| Audience | Academic |
| Author | Mijangos, E. |
| Author_xml | – sequence: 1 givenname: E. surname: Mijangos fullname: Mijangos, E. email: eugenio.mijangos@ehu.es organization: Department of Applied Mathematics and Statistics and Operations Research, University of the Basque Country UPV/EHU |
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| CitedBy_id | crossref_primary_10_1016_j_compchemeng_2018_01_017 crossref_primary_10_1007_s10479_018_3032_7 crossref_primary_10_1007_s11081_020_09563_2 crossref_primary_10_1007_s10898_019_00820_y crossref_primary_10_1007_s10898_020_00986_w crossref_primary_10_1007_s10898_019_00816_8 crossref_primary_10_1007_s10898_024_01433_w |
| Cites_doi | 10.1016/S0377-2217(02)00628-8 10.1023/A:1011241421041 10.1016/j.omega.2004.05.001 10.1515/9781400873173 10.1023/A:1013827731218 10.1016/j.cor.2011.06.021 10.1007/978-3-642-46216-0 10.1137/0114008 10.1016/j.cor.2008.11.011 10.1287/opre.50.3.415.7751 10.1016/0305-0548(94)90024-8 10.1016/j.compchemeng.2003.11.003 10.1016/j.disopt.2006.10.011 10.1016/j.ejor.2009.09.027 10.1007/s10107-006-0724-6 10.1007/s10107-005-0592-5 10.1093/oso/9780195100563.001.0001 10.1137/1.9780898718799 10.1007/978-3-642-36062-6_18 10.1007/978-3-642-36062-6_51 |
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| DOI | 10.1007/s10479-015-1899-0 |
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| Keywords | Outer approximation Mixed-integer nonlinear programming Quadratic programming Convex programming Branch-and-fix coordination method Stochastic programming |
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| SubjectTerms | Algorithms Approximation Business and Management Combinatorics Convex functions Integer programming Mathematical analysis Mathematical models Mathematical research Nonlinear programming Nonlinearity Operations research Operations Research/Decision Theory Quadratic programming Stochastic processes Stochasticity Strategy Studies Texts Theory of Computation Variables |
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| Title | An algorithm for two-stage stochastic mixed-integer nonlinear convex problems |
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