An accelerated extended cutting plane approach with piecewise linear approximations for signomial geometric programming

This paper presents a global optimization approach for solving signomial geometric programming (SGP) problems. We employ an accelerated extended cutting plane (ECP) approach integrated with piecewise linear (PWL) approximations to solve the global optimization of SGP problems. In this approach, we s...

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Published in:	Journal of global optimization Vol. 70; no. 3; pp. 579 - 599
Main Authors:	Zhan, Yiduo, Zheng, Qipeng P., Tseng, Chung-Li, Pasiliao, Eduardo L.
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.03.2018 Springer Springer Nature B.V
Subjects:	Algorithms Approximation Computer Science Cutting Economic models Global optimization Mathematical programming Mathematics Mathematics and Statistics Methods Mixed integer Nonlinear programming Operations Research/Decision Theory Optimization Real Functions Piecewise linear approximation Signomial geometric programming Accelerated extended cutting plane Mixed-integer linear programming
ISSN:	0925-5001, 1573-2916
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Abstract	This paper presents a global optimization approach for solving signomial geometric programming (SGP) problems. We employ an accelerated extended cutting plane (ECP) approach integrated with piecewise linear (PWL) approximations to solve the global optimization of SGP problems. In this approach, we separate the feasible regions determined by the constraints into convex and nonconvex ones in the logarithmic domain. In the nonconvex feasible regions, the corresponding constraint functions are converted into mixed integer linear constraints using PWL approximations, while the other constraints with convex feasible regions are handled by the ECP method. We also use pre-processed initial cuts and batched cuts to accelerate the proposed algorithm. Numerical results show that the proposed approach can solve the global optimization of SGP problems efficiently and effectively.
AbstractList	This paper presents a global optimization approach for solving signomial geometric programming (SGP) problems. We employ an accelerated extended cutting plane (ECP) approach integrated with piecewise linear (PWL) approximations to solve the global optimization of SGP problems. In this approach, we separate the feasible regions determined by the constraints into convex and nonconvex ones in the logarithmic domain. In the nonconvex feasible regions, the corresponding constraint functions are converted into mixed integer linear constraints using PWL approximations, while the other constraints with convex feasible regions are handled by the ECP method. We also use pre-processed initial cuts and batched cuts to accelerate the proposed algorithm. Numerical results show that the proposed approach can solve the global optimization of SGP problems efficiently and effectively.
Audience	Academic
Author	Zheng, Qipeng P. Pasiliao, Eduardo L. Tseng, Chung-Li Zhan, Yiduo
Author_xml	– sequence: 1 givenname: Yiduo surname: Zhan fullname: Zhan, Yiduo organization: Department of Industrial Engineering and Management Systems, University of Central Florida – sequence: 2 givenname: Qipeng P. orcidid: 0000-0002-4597-3426 surname: Zheng fullname: Zheng, Qipeng P. email: Qipeng.Zheng@ucf.edu organization: Department of Industrial Engineering and Management Systems, University of Central Florida – sequence: 3 givenname: Chung-Li surname: Tseng fullname: Tseng, Chung-Li organization: UNSW Business School, UNSW – sequence: 4 givenname: Eduardo L. surname: Pasiliao fullname: Pasiliao, Eduardo L. organization: Air Force Research Laboratory
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Cites_doi	10.1007/s10898-006-9091-3 10.1016/j.ejor.2011.06.046 10.1016/0045-7949(86)90327-5 10.1016/j.ejor.2015.01.038 10.1017/CBO9780511804441 10.1287/opre.32.1.70 10.1016/S0098-1354(97)00000-8 10.1080/10556780802702278 10.1016/j.ejor.2004.12.002 10.1080/095372897234948 10.1137/0108053 10.1016/S0098-1354(96)00282-7 10.1016/S0893-9659(98)00179-7 10.1016/j.ejor.2013.10.016 10.1109/JSAC.2004.837347 10.1287/opre.1080.0586 10.1007/s10898-005-2098-3 10.1016/j.cam.2007.01.039 10.1016/j.compchemeng.2005.04.004 10.1021/ie0402719 10.1016/0167-6377(88)90071-5 10.1016/j.ejor.2005.11.037 10.1007/BF01580667 10.1109/7693.975444 10.1016/0098-1354(95)00164-W
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Keywords	Piecewise linear approximation Signomial geometric programming Accelerated extended cutting plane Mixed-integer linear programming
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Snippet	This paper presents a global optimization approach for solving signomial geometric programming (SGP) problems. We employ an accelerated extended cutting plane...
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SubjectTerms	Algorithms Approximation Computer Science Cutting Economic models Global optimization Mathematical programming Mathematics Mathematics and Statistics Methods Mixed integer Nonlinear programming Operations Research/Decision Theory Optimization Real Functions
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Title	An accelerated extended cutting plane approach with piecewise linear approximations for signomial geometric programming
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