| A New Subdivision Algorithm for the Bernstein Polynomial Approach to Global Optimization |
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| 引用本文： | P. S. V. Nataraj M. Arounassalame. A New Subdivision Algorithm for the Bernstein Polynomial Approach to Global Optimization[J]. 国际自动化与计算杂志, 2007, 4(4): 342-352. DOI: 10.1007/s11633-007-0342-7 |
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| 作者姓名： | P. S. V. Nataraj M. Arounassalame |
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| 作者单位： | Systems and Control Engineering ACRE Building，Indian Institute of Technology Bombay，Powai，Mumbai 400076，India，Systems and Control Engineering，ACRE Building，Indian Institute of Technology Bombay，Powai，Mumbai 400076，India |
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| 摘 要： | In this paper,an improved algorithm is proposed for unconstrained global optimization to tackle non-convex nonlinear multivariate polynomial programming problems.The proposed algorithm is based on the Bernstein polynomial approach.Novel features of the proposed algorithm are that it uses a new rule for the selection of the subdivision point,modified rules for the selection of the subdivision direction,and a new acceleration device to avoid some unnecessary subdivisions.The performance of the proposed algorithm is numerically tested on a collection of 16 test problems.The results of the tests show the proposed algorithm to be superior to the existing Bernstein algorithm in terms of the chosen performance metrics.
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| 关 键 词： | Bernstein多项式 整体优化 非线性优化 多项式 |
| 收稿时间： | 2007-02-26 |
| 修稿时间： | 2007-02-26 |
A new subdivision algorithm for the Bernstein polynomial approach to global optimization |
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| P. S. V. Nataraj,M. Arounassalame. A new subdivision algorithm for the Bernstein polynomial approach to global optimization[J]. International Journal of Automation and computing, 2007, 4(4): 342-352. DOI: 10.1007/s11633-007-0342-7 |
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| Authors: | P. S. V. Nataraj M. Arounassalame |
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| Affiliation: | (1) Systems and Control Engineering, ACRE Building, Indian Institute of Technology Bombay, Powai, Mumbai, 400 076, India |
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| Abstract: | In this paper,an improved algorithm is proposed for unconstrained global optimization to tackle non-convex nonlinear multivariate polynomial programming problems.The proposed algorithm is based on the Bernstein polynomial approach.Novel features of the proposed algorithm are that it uses a new rule for the selection of the subdivision point,modified rules for the selection of the subdivision direction,and a new acceleration device to avoid some unnecessary subdivisions.The performance of the proposed algorithm is numerically tested on a collection of 16 test problems.The results of the tests show the proposed algorithm to be superior to the existing Bernstein algorithm in terms of the chosen performance metrics. |
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| Keywords: | Bernstein polynomials global optimization nonlinear optimization polynomial optimization unconstrained optimization |
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