Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/286958 
Authors: 
Year of Publication: 
2021
Citation: 
[Journal:] Optimization Letters [ISSN:] 1862-4480 [Volume:] 16 [Issue:] 2 [Publisher:] Springer [Place:] Berlin, Heidelberg [Year:] 2021 [Pages:] 635-652
Publisher: 
Springer, Berlin, Heidelberg
Abstract: 
We investigate the generalized red refinement for n-dimensional simplices that dates back to Freudenthal (Ann Math 43(3):580–582, 1942) in a mixed-integer nonlinear program (MINLP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\textsc {MINLP}}$$\end{document}) context. We show that the red refinement meets sufficient convergence conditions for a known MINLP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\textsc {MINLP}}$$\end{document} solution framework that is essentially based on solving piecewise linear relaxations. In addition, we prove that applying this refinement procedure results in piecewise linear relaxations that can be modeled by the well-known incremental method established by Markowitz and Manne (Econometrica 25(1):84–110, 1957). Finally, numerical results from the field of alternating current optimal power flow demonstrate the applicability of the red refinement in such MIP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\textsc {MIP}}$$\end{document}-based MINLP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\textsc {MINLP}}$$\end{document} solution frameworks.
Subjects: 
Mixed-integer nonlinear programming
Red refinement
Piecewise linear relaxation
Incremental method
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Document Type: 
Article
Document Version: 
Published Version

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