Improved Lipschitz bounds with the first norm for function values over multidimensional simplex
A branch and bound algorithm for global optimization is proposed, where the maximum of an upper bounding function based on Lipschitz condition and the first norm over a simplex is used as the upper bound of function. In this case the graph of bounding function is intersection of n‐dimensional pyrami...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2008-12-01
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| Series: | Mathematical Modelling and Analysis |
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| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/7045 |
| _version_ | 1819225553273618432 |
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| author | Remigijus Paulavičius Julius Žilinskas |
| author_facet | Remigijus Paulavičius Julius Žilinskas |
| author_sort | Remigijus Paulavičius |
| collection | DOAJ |
| description | A branch and bound algorithm for global optimization is proposed, where the maximum of an upper bounding function based on Lipschitz condition and the first norm over a simplex is used as the upper bound of function. In this case the graph of bounding function is intersection of n‐dimensional pyramids and its maximum point is found solving a system of linear equations. The efficiency of the proposed global optimization algorithm is evaluated experimentally.
First Published Online: 14 Oct 2010 |
| first_indexed | 2024-12-23T10:11:25Z |
| format | Article |
| id | doaj.art-f96d216ce713463ea5e510635db42a96 |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-12-23T10:11:25Z |
| publishDate | 2008-12-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-f96d216ce713463ea5e510635db42a962022-12-21T17:50:56ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102008-12-0113410.3846/1392-6292.2008.13.553-563Improved Lipschitz bounds with the first norm for function values over multidimensional simplexRemigijus Paulavičius0Julius Žilinskas1Institute of Mathematics and Informatics, Akademijos 4, LT-08663, Vilnius, LithuaniaInstitute of Mathematics and Informatics, Akademijos 4, LT-08663, Vilnius, LithuaniaA branch and bound algorithm for global optimization is proposed, where the maximum of an upper bounding function based on Lipschitz condition and the first norm over a simplex is used as the upper bound of function. In this case the graph of bounding function is intersection of n‐dimensional pyramids and its maximum point is found solving a system of linear equations. The efficiency of the proposed global optimization algorithm is evaluated experimentally. First Published Online: 14 Oct 2010https://journals.vgtu.lt/index.php/MMA/article/view/7045global optimizationbranch and bound algorithmsLipschitz optimizationthe first norm |
| spellingShingle | Remigijus Paulavičius Julius Žilinskas Improved Lipschitz bounds with the first norm for function values over multidimensional simplex Mathematical Modelling and Analysis global optimization branch and bound algorithms Lipschitz optimization the first norm |
| title | Improved Lipschitz bounds with the first norm for function values over multidimensional simplex |
| title_full | Improved Lipschitz bounds with the first norm for function values over multidimensional simplex |
| title_fullStr | Improved Lipschitz bounds with the first norm for function values over multidimensional simplex |
| title_full_unstemmed | Improved Lipschitz bounds with the first norm for function values over multidimensional simplex |
| title_short | Improved Lipschitz bounds with the first norm for function values over multidimensional simplex |
| title_sort | improved lipschitz bounds with the first norm for function values over multidimensional simplex |
| topic | global optimization branch and bound algorithms Lipschitz optimization the first norm |
| url | https://journals.vgtu.lt/index.php/MMA/article/view/7045 |
| work_keys_str_mv | AT remigijuspaulavicius improvedlipschitzboundswiththefirstnormforfunctionvaluesovermultidimensionalsimplex AT juliuszilinskas improvedlipschitzboundswiththefirstnormforfunctionvaluesovermultidimensionalsimplex |