Academic Journal
Two methods based on second-order dynamical systems for solving a special class of nonlinear optimization problems.
| Τίτλος: | Two methods based on second-order dynamical systems for solving a special class of nonlinear optimization problems. |
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| Συγγραφείς: | Sun, Juhe, Huang, Guolin, Wang, Li, Ma, Ning |
| Πηγή: | Electronic Research Archive; 2026, Vol. 34 Issue 3, p1-31, 31p |
| Θεματικοί όροι: | Nonlinear programming, Dynamic models, Stability theory, Numerical analysis, Approximation theory, Discontinuous functions |
| Περίληψη: | Symbolic functions, as an important class of nonsmooth functions, play a key role in many fields such as system control and optimization theory. In this study, the special case of nonlinear optimization problems with sign function constraints is discussed in depth. Based on the smooth approximation theory, the study first adopts an approximate substitution method to smooth the nonsmooth constraints and then transforms them into differentiable optimization problems, thus effectively avoiding the numerical computational difficulties caused by the sign function. Second, the constrained optimization problem is transformed into an unconstrained optimization problem by constructing an exact penalty function. Third, two forms of second-order dynamical systems are established to solve the problem, and a rigorous theoretical analysis of the stability of these systems is conducted. Finally, the convergence and computational efficiency of the proposed method are verified by numerical simulation experiments of the system, and the simulation results fully prove the effectiveness and practicality of the algorithm. [ABSTRACT FROM AUTHOR] |
| Copyright of Electronic Research Archive is the property of American Institute of Mathematical Sciences 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.) | |
| Βάση Δεδομένων: | Complementary Index |
| FullText | Text: Availability: 0 |
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| Header | DbId: edb DbLabel: Complementary Index An: 192210178 RelevancyScore: 1041 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 1041.07177734375 |
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| Items | – Name: Title Label: Title Group: Ti Data: Two methods based on second-order dynamical systems for solving a special class of nonlinear optimization problems. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Sun%2C+Juhe%22">Sun, Juhe</searchLink><br /><searchLink fieldCode="AR" term="%22Huang%2C+Guolin%22">Huang, Guolin</searchLink><br /><searchLink fieldCode="AR" term="%22Wang%2C+Li%22">Wang, Li</searchLink><br /><searchLink fieldCode="AR" term="%22Ma%2C+Ning%22">Ma, Ning</searchLink> – Name: TitleSource Label: Source Group: Src Data: Electronic Research Archive; 2026, Vol. 34 Issue 3, p1-31, 31p – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Nonlinear+programming%22">Nonlinear programming</searchLink><br /><searchLink fieldCode="DE" term="%22Dynamic+models%22">Dynamic models</searchLink><br /><searchLink fieldCode="DE" term="%22Stability+theory%22">Stability theory</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Approximation+theory%22">Approximation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Discontinuous+functions%22">Discontinuous functions</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Symbolic functions, as an important class of nonsmooth functions, play a key role in many fields such as system control and optimization theory. In this study, the special case of nonlinear optimization problems with sign function constraints is discussed in depth. Based on the smooth approximation theory, the study first adopts an approximate substitution method to smooth the nonsmooth constraints and then transforms them into differentiable optimization problems, thus effectively avoiding the numerical computational difficulties caused by the sign function. Second, the constrained optimization problem is transformed into an unconstrained optimization problem by constructing an exact penalty function. Third, two forms of second-order dynamical systems are established to solve the problem, and a rigorous theoretical analysis of the stability of these systems is conducted. Finally, the convergence and computational efficiency of the proposed method are verified by numerical simulation experiments of the system, and the simulation results fully prove the effectiveness and practicality of the algorithm. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Group: Ab Data: <i>Copyright of Electronic Research Archive is the property of American Institute of Mathematical Sciences 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: Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 31 StartPage: 1 Subjects: – SubjectFull: Nonlinear programming Type: general – SubjectFull: Dynamic models Type: general – SubjectFull: Stability theory Type: general – SubjectFull: Numerical analysis Type: general – SubjectFull: Approximation theory Type: general – SubjectFull: Discontinuous functions Type: general Titles: – TitleFull: Two methods based on second-order dynamical systems for solving a special class of nonlinear optimization problems. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Sun, Juhe – PersonEntity: Name: NameFull: Huang, Guolin – PersonEntity: Name: NameFull: Wang, Li – PersonEntity: Name: NameFull: Ma, Ning IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 03 Text: 2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 26881594 Numbering: – Type: volume Value: 34 – Type: issue Value: 3 Titles: – TitleFull: Electronic Research Archive Type: main |
| ResultId | 1 |