On Solving Nonsmooth Mixed-Integer Nonlinear Programming Problems by Outer Approximation and Generalized Benders Decomposition
In this paper, we mainly study nonsmooth mixed-integer nonlinear programming problems and solution algorithms by outer approximation and generalized Benders decomposition. Outer approximation and generalized Benders algorithms are provided to solve these problems with nonsmooth convex functions and...
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| Vydané v: | Journal of optimization theory and applications Ročník 181; číslo 3; s. 840 - 863 |
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| Hlavní autori: | , , , , |
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| Jazyk: | English |
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New York
Springer US
01.06.2019
Springer Nature B.V |
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| ISSN: | 0022-3239, 1573-2878 |
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| Abstract | In this paper, we mainly study nonsmooth mixed-integer nonlinear programming problems and solution algorithms by outer approximation and generalized Benders decomposition. Outer approximation and generalized Benders algorithms are provided to solve these problems with nonsmooth convex functions and with conic constraint, respectively. We illustrate these two algorithms by providing detailed procedure of solving several examples. The numerical examples show that outer approximation and generalized Benders decomposition provide a feasible alternative for solving such problems without differentiability. |
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| AbstractList | In this paper, we mainly study nonsmooth mixed-integer nonlinear programming problems and solution algorithms by outer approximation and generalized Benders decomposition. Outer approximation and generalized Benders algorithms are provided to solve these problems with nonsmooth convex functions and with conic constraint, respectively. We illustrate these two algorithms by providing detailed procedure of solving several examples. The numerical examples show that outer approximation and generalized Benders decomposition provide a feasible alternative for solving such problems without differentiability. |
| Author | Xu, Liang Zeng, Bo Wei, Zhou Ali, M. Montaz Yao, Jen-Chih |
| Author_xml | – sequence: 1 givenname: Zhou surname: Wei fullname: Wei, Zhou organization: Department of Mathematics, Yunnan University – sequence: 2 givenname: M. Montaz surname: Ali fullname: Ali, M. Montaz organization: School of Computer Science and Applied Mathematics, University of the Witwatersrand – sequence: 3 givenname: Liang orcidid: 0000-0003-2890-4872 surname: Xu fullname: Xu, Liang organization: Department of Industrial Engineering, University of Pittsburgh – sequence: 4 givenname: Bo surname: Zeng fullname: Zeng, Bo organization: Department of Industrial Engineering, University of Pittsburgh – sequence: 5 givenname: Jen-Chih surname: Yao fullname: Yao, Jen-Chih email: yaojc@mail.cmu.edu.tw organization: Department of Mathematics, Zhejiang Normal University, Research Center for Interneural Computing, China Medical University Hospital, China Medical University |
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| CitedBy_id | crossref_primary_10_1016_j_ces_2022_117939 crossref_primary_10_1007_s10957_022_02114_y crossref_primary_10_1016_j_compchemeng_2023_108467 crossref_primary_10_1016_j_orl_2025_107243 crossref_primary_10_1137_23M1592493 crossref_primary_10_1016_j_asoc_2022_109018 crossref_primary_10_1016_j_energy_2021_122913 crossref_primary_10_1016_j_enconman_2025_120402 |
| Cites_doi | 10.1007/s10957-015-0715-y 10.1023/A:1011241421041 10.1287/opre.1060.0371 10.1137/140967519 10.1007/BF01386316 10.1016/0098-1354(89)87017-6 10.1080/02331934.2012.712118 10.1287/mnsc.31.12.1533 10.1007/978-3-662-21569-2 10.1007/978-1-4757-3532-1 10.1016/j.ejor.2015.12.018 10.1002/9781118033036 10.1007/s10107-004-0503-1 10.1016/j.compchemeng.2005.07.012 10.1007/s10898-015-0284-5 10.1016/0098-1354(95)87027-X 10.1007/BF01581153 10.1007/s10107-003-0375-9 10.1016/j.disopt.2006.10.011 10.1023/A:1021039126272 10.1142/5021 10.1007/BF00934810 10.1007/BF02592064 10.1007/s10107-005-0581-8 10.1007/s10957-011-9888-1 10.1007/978-1-4614-1927-3_2 |
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| Keywords | Subgradient Generalized Benders decomposition 90C30 Mixed-integer nonlinear programming 90C25 90C11 Master program Outer approximation |
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| SubjectTerms | Algorithms Applications of Mathematics Approximation Benders decomposition Calculus of Variations and Optimal Control; Optimization Decomposition Engineering Feasibility Mathematical analysis Mathematics Mathematics and Statistics Nonlinear programming Operations Research/Decision Theory Optimization Theory of Computation |
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| Title | On Solving Nonsmooth Mixed-Integer Nonlinear Programming Problems by Outer Approximation and Generalized Benders Decomposition |
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