A generalization of ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega $$\end{document}-subdivision ensuring convergence of the simplicial algorithm

被引：0
作者：
Takahito Kuno
Tomohiro Ishihama
机构：
[1] University of Tsukuba,Graduate School of Systems and Information Engineering
[2] NS Solutions Corporation,undefined
来源：
Computational Optimization and Applications | 2016年 / 64卷 / 2期
关键词：
Global optimization; Strictly convex maximization; Branch-and-bound; Simplicial algorithm; -subdivision;
D O I：
10.1007/s10589-015-9817-6
中图分类号：
学科分类号：
摘要：
In this paper, we refine the proof of convergence by Kuno–Buckland (J Global Optim 52:371–390, 2012) for the simplicial algorithm with ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega $$\end{document}-subdivision and generalize their ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega $$\end{document}-bisection rule to establish a class of subdivision rules, called ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega $$\end{document}-k-section, which bounds the number of subsimplices generated in a single execution of subdivision by a prescribed number k. We also report some numerical results of comparing the ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega $$\end{document}-k-section rule with the usual ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega $$\end{document}-subdivision rule.
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页码：535 / 555
页数：20
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  • [15] Thoai NV(undefined)-subdivisions undefined undefined undefined-undefined
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