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A global optimization method based on multi-unit extremum-seeking for scalar nonlinear systems

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Title: A global optimization method based on multi-unit extremum-seeking for scalar nonlinear systems
Authors: Esmaeilzadeh Azar, F. farhad.esmaeilzadeh-azar@polymtl.ca, Perrier, M. michel.perrier@polymtl.ca, Srinivasan, B. bala.srinivasan@polymtl.ca
Source: Computers & Chemical Engineering. Mar2011, Vol. 35 Issue 3, p456-463. 8p.
Subjects: Nonlinear systems, Nonlinear functional analysis, Combinatorial optimization, Finite differences, Continuous functions, Real-time computing, Automatic control systems
Abstract: Abstract: Finding the global optimum of a nonlinear function is a challenging task that could involve a large number of functional evaluations. In this paper, an algorithm that uses tools from the domain of extremum-seeking is shown to provide an efficient deterministic method for global optimization. Extremum-seeking schemes typically find the local optimum by controlling the gradient to zero. In this paper, the multi-unit framework is used, where the gradient is estimated by finite difference for a given offset between the inputs. The gradient is pushed to zero by an integral controller. It is shown that if the offset is reduced to zero, the system can be made to converge to the global optimum of nonlinear continuous static, scalar maps. The result is extended to constrained problems where a switching control strategy is employed. Several illustrative examples are presented and the proposed method is compared with other methods of global optimization. [Copyright &y& Elsevier]
Copyright of Computers & Chemical Engineering is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: <searchLink fieldCode="JN" term="%22Computers+%26+Chemical+Engineering%22">Computers & Chemical Engineering</searchLink>. Mar2011, Vol. 35 Issue 3, p456-463. 8p.
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  Data: <searchLink fieldCode="DE" term="%22Nonlinear+systems%22">Nonlinear systems</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+functional+analysis%22">Nonlinear functional analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Combinatorial+optimization%22">Combinatorial optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+differences%22">Finite differences</searchLink><br /><searchLink fieldCode="DE" term="%22Continuous+functions%22">Continuous functions</searchLink><br /><searchLink fieldCode="DE" term="%22Real-time+computing%22">Real-time computing</searchLink><br /><searchLink fieldCode="DE" term="%22Automatic+control+systems%22">Automatic control systems</searchLink>
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  Data: Abstract: Finding the global optimum of a nonlinear function is a challenging task that could involve a large number of functional evaluations. In this paper, an algorithm that uses tools from the domain of extremum-seeking is shown to provide an efficient deterministic method for global optimization. Extremum-seeking schemes typically find the local optimum by controlling the gradient to zero. In this paper, the multi-unit framework is used, where the gradient is estimated by finite difference for a given offset between the inputs. The gradient is pushed to zero by an integral controller. It is shown that if the offset is reduced to zero, the system can be made to converge to the global optimum of nonlinear continuous static, scalar maps. The result is extended to constrained problems where a switching control strategy is employed. Several illustrative examples are presented and the proposed method is compared with other methods of global optimization. [Copyright &y& Elsevier]
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  Data: <i>Copyright of Computers & Chemical Engineering is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – SubjectFull: Nonlinear functional analysis
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      – SubjectFull: Combinatorial optimization
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