Convex mixed integer nonlinear programming problems and an outer approximation algorithm

In this paper, we mainly study one class of convex mixed-integer nonlinear programming problems (MINLPs) with non-differentiable data. By dropping the differentiability assumption, we substitute gradients with subgradients obtained from KKT conditions, and use the outer approximation method to refor...

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Published in:	Journal of global optimization Vol. 63; no. 2; pp. 213 - 227
Main Authors:	Wei, Zhou, Ali, M. Montaz
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.10.2015 Springer Springer Nature B.V
Subjects:	Algorithms Applied mathematics Approximation Computer Science Convergence Convex analysis Equivalence Integer programming Mathematical analysis Mathematics Mathematics and Statistics Mixed integer Nonlinear programming Operations Research/Decision Theory Optimization Optimization algorithms Real Functions Variables Convex MINLP 90C30 90C25 90C11 Master program Decomposition Outer approximation
ISSN:	0925-5001, 1573-2916
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Abstract	In this paper, we mainly study one class of convex mixed-integer nonlinear programming problems (MINLPs) with non-differentiable data. By dropping the differentiability assumption, we substitute gradients with subgradients obtained from KKT conditions, and use the outer approximation method to reformulate convex MINLP as one equivalent MILP master program. By solving a finite sequence of subproblems and relaxed MILP problems, we establish an outer approximation algorithm to find the optimal solution of this convex MINLP. The convergence of this algorithm is also presented. The work of this paper generalizes and extends the outer approximation method in the sense of dealing with convex MINLPs from differentiable case to non-differentiable one.
AbstractList	In this paper, we mainly study one class of convex mixed-integer nonlinear programming problems (MINLPs) with non-differentiable data. By dropping the differentiability assumption, we substitute gradients with subgradients obtained from KKT conditions, and use the outer approximation method to reformulate convex MINLP as one equivalent MILP master program. By solving a finite sequence of subproblems and relaxed MILP problems, we establish an outer approximation algorithm to find the optimal solution of this convex MINLP. The convergence of this algorithm is also presented. The work of this paper generalizes and extends the outer approximation method in the sense of dealing with convex MINLPs from differentiable case to non-differentiable one.
Audience	Academic
Author	Ali, M. Montaz Wei, Zhou
Author_xml	– sequence: 1 givenname: Zhou surname: Wei fullname: Wei, Zhou email: wzhou@ynu.edu.cn organization: Department of Mathematics, Yunnan University – sequence: 2 givenname: M. Montaz surname: Ali fullname: Ali, M. Montaz organization: School of Computational and Applied Mathematics, University of the Witwatersrand, TCSE, Faculty of Engineering and Built Environment, University of the Witwatersrand
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CitedBy_id	crossref_primary_10_1007_s10957_022_02114_y crossref_primary_10_1016_j_orl_2025_107243 crossref_primary_10_1007_s10898_020_00906_y crossref_primary_10_1016_j_ejor_2025_07_016 crossref_primary_10_1080_02331934_2018_1434173 crossref_primary_10_1137_140967519 crossref_primary_10_1007_s10957_019_01499_7 crossref_primary_10_23919_JSEE_2023_000040
Cites_doi	10.1007/s10898-006-9005-4 10.1007/s10107-003-0467-6 10.1007/BF01582893 10.1007/BF01580620 10.1007/BF01581153 10.1007/978-1-4757-3532-1 10.1007/BF02592064 10.1007/BF00934810 10.1142/5021 10.1007/s10100-007-0051-x 10.1080/02331934.2012.712118 10.1093/oso/9780195100563.001.0001 10.1007/978-3-662-21569-2 10.1007/s10957-015-0715-y 10.1016/0098-1354(95)87027-X 10.1007/978-1-4614-1927-3_2 10.1016/j.disopt.2006.10.011 10.1023/A:1011241421041 10.1016/j.compchemeng.2005.07.012 10.1023/A:1021039126272 10.1023/A:1021091110342
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Snippet	In this paper, we mainly study one class of convex mixed-integer nonlinear programming problems (MINLPs) with non-differentiable data. By dropping the...
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SubjectTerms	Algorithms Applied mathematics Approximation Computer Science Convergence Convex analysis Equivalence Integer programming Mathematical analysis Mathematics Mathematics and Statistics Mixed integer Nonlinear programming Operations Research/Decision Theory Optimization Optimization algorithms Real Functions Variables
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Title	Convex mixed integer nonlinear programming problems and an outer approximation algorithm
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