Canonical dual least square method for solving general nonlinear systems of quadratic equations.
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| Title: | Canonical dual least square method for solving general nonlinear systems of quadratic equations. |
|---|---|
| Authors: | Ruan, N.1, Gao, David1 gao@vt.edu, Jiao, Y.2 |
| Source: | Computational Optimization & Applications. Oct2010, Vol. 47 Issue 2, p335-347. 13p. 3 Graphs. |
| Subjects: | Contact transformations, Least squares, Nonlinear systems, Quadratic equations, Nonconvex programming, Duality theory (Mathematics) |
| Abstract: | This paper presents a canonical dual approach for solving general nonlinear algebraic systems. By using least square method, the nonlinear system of m-quadratic equations in n-dimensional space is first formulated as a nonconvex optimization problem. We then proved that, by the canonical duality theory developed by the second author, this nonconvex problem is equivalent to a concave maximization problem in ℝ, which can be solved easily by well-developed convex optimization techniques. Both existence and uniqueness of global optimal solutions are discussed, and several illustrative examples are presented. [ABSTRACT FROM AUTHOR] |
| Copyright of Computational Optimization & Applications is the property of Springer Nature 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.) | |
| Database: | Engineering Source |
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| Items | – Name: Title Label: Title Group: Ti Data: Canonical dual least square method for solving general nonlinear systems of quadratic equations. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Ruan%2C+N%2E%22">Ruan, N.</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Gao%2C+David%22">Gao, David</searchLink><relatesTo>1</relatesTo><i> gao@vt.edu</i><br /><searchLink fieldCode="AR" term="%22Jiao%2C+Y%2E%22">Jiao, Y.</searchLink><relatesTo>2</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Computational+Optimization+%26+Applications%22">Computational Optimization & Applications</searchLink>. Oct2010, Vol. 47 Issue 2, p335-347. 13p. 3 Graphs. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Contact+transformations%22">Contact transformations</searchLink><br /><searchLink fieldCode="DE" term="%22Least+squares%22">Least squares</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+systems%22">Nonlinear systems</searchLink><br /><searchLink fieldCode="DE" term="%22Quadratic+equations%22">Quadratic equations</searchLink><br /><searchLink fieldCode="DE" term="%22Nonconvex+programming%22">Nonconvex programming</searchLink><br /><searchLink fieldCode="DE" term="%22Duality+theory+%28Mathematics%29%22">Duality theory (Mathematics)</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper presents a canonical dual approach for solving general nonlinear algebraic systems. By using least square method, the nonlinear system of m-quadratic equations in n-dimensional space is first formulated as a nonconvex optimization problem. We then proved that, by the canonical duality theory developed by the second author, this nonconvex problem is equivalent to a concave maximization problem in ℝ, which can be solved easily by well-developed convex optimization techniques. Both existence and uniqueness of global optimal solutions are discussed, and several illustrative examples are presented. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Computational Optimization & Applications is the property of Springer Nature 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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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s10589-008-9222-5 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 13 StartPage: 335 Subjects: – SubjectFull: Contact transformations Type: general – SubjectFull: Least squares Type: general – SubjectFull: Nonlinear systems Type: general – SubjectFull: Quadratic equations Type: general – SubjectFull: Nonconvex programming Type: general – SubjectFull: Duality theory (Mathematics) Type: general Titles: – TitleFull: Canonical dual least square method for solving general nonlinear systems of quadratic equations. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Ruan, N. – PersonEntity: Name: NameFull: Gao, David – PersonEntity: Name: NameFull: Jiao, Y. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 10 Text: Oct2010 Type: published Y: 2010 Identifiers: – Type: issn-print Value: 09266003 Numbering: – Type: volume Value: 47 – Type: issue Value: 2 Titles: – TitleFull: Computational Optimization & Applications Type: main |
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