Academic Journal
Optimization-Constrained Differential Equations with Active Set Changes.
| Τίτλος: | Optimization-Constrained Differential Equations with Active Set Changes. |
|---|---|
| Συγγραφείς: | Stechlinski, Peter |
| Πηγή: | Journal of Optimization Theory & Applications; Oct2020, Vol. 187 Issue 1, p266-293, 28p |
| Θεματικοί όροι: | Differential equations, Nonlinear differential equations, Differential-algebraic equations, Nonlinear equations, Smoothness of functions, Algebraic equations |
| Περίληψη: | Foundational theory is established for nonlinear differential equations with embedded nonlinear optimization problems exhibiting active set changes. Existence, uniqueness, and continuation of solutions are shown, followed by lexicographically smooth (implying Lipschitzian) parametric dependence. The sensitivity theory found here accurately characterizes sensitivity jumps resulting from active set changes via an auxiliary nonsmooth sensitivity system obtained by lexicographic directional differentiation. The results in this article hold under easily verifiable regularity conditions (linear independence of constraints and strong second-order sufficiency), which are shown to imply generalized differentiation index one of a nonsmooth differential-algebraic equation system obtained by replacing the optimization problem with its optimality conditions and recasting the complementarity conditions as nonsmooth algebraic equations. The theory in this article is computationally relevant, allowing for implementation of dynamic optimization strategies (i.e., open-loop optimal control), and recovers (and rigorously formalizes) classical results in the absence of active set changes. Along the way, contributions are made to the theory of piecewise differentiable functions. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Optimization Theory & 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.) | |
| Βάση Δεδομένων: | Complementary Index |
| FullText | Links: – Type: other Text: Availability: 0 CustomLinks: – Url: https://dx.doi.org/doi:10.1007/s10957-020-01744-4 Name: EDS - Springer Nature Journals (s7799221) Category: fullText Text: View record at Springer |
|---|---|
| Header | DbId: edb DbLabel: Complementary Index An: 146476395 RelevancyScore: 886 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 885.839599609375 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: Optimization-Constrained Differential Equations with Active Set Changes. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Stechlinski%2C+Peter%22">Stechlinski, Peter</searchLink> – Name: TitleSource Label: Source Group: Src Data: Journal of Optimization Theory & Applications; Oct2020, Vol. 187 Issue 1, p266-293, 28p – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Differential+equations%22">Differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+differential+equations%22">Nonlinear differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Differential-algebraic+equations%22">Differential-algebraic equations</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+equations%22">Nonlinear equations</searchLink><br /><searchLink fieldCode="DE" term="%22Smoothness+of+functions%22">Smoothness of functions</searchLink><br /><searchLink fieldCode="DE" term="%22Algebraic+equations%22">Algebraic equations</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Foundational theory is established for nonlinear differential equations with embedded nonlinear optimization problems exhibiting active set changes. Existence, uniqueness, and continuation of solutions are shown, followed by lexicographically smooth (implying Lipschitzian) parametric dependence. The sensitivity theory found here accurately characterizes sensitivity jumps resulting from active set changes via an auxiliary nonsmooth sensitivity system obtained by lexicographic directional differentiation. The results in this article hold under easily verifiable regularity conditions (linear independence of constraints and strong second-order sufficiency), which are shown to imply generalized differentiation index one of a nonsmooth differential-algebraic equation system obtained by replacing the optimization problem with its optimality conditions and recasting the complementarity conditions as nonsmooth algebraic equations. The theory in this article is computationally relevant, allowing for implementation of dynamic optimization strategies (i.e., open-loop optimal control), and recovers (and rigorously formalizes) classical results in the absence of active set changes. Along the way, contributions are made to the theory of piecewise differentiable functions. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Group: Ab Data: <i>Copyright of Journal of Optimization Theory & 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.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edb&AN=146476395 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s10957-020-01744-4 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 28 StartPage: 266 Subjects: – SubjectFull: Differential equations Type: general – SubjectFull: Nonlinear differential equations Type: general – SubjectFull: Differential-algebraic equations Type: general – SubjectFull: Nonlinear equations Type: general – SubjectFull: Smoothness of functions Type: general – SubjectFull: Algebraic equations Type: general Titles: – TitleFull: Optimization-Constrained Differential Equations with Active Set Changes. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Stechlinski, Peter IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 10 Text: Oct2020 Type: published Y: 2020 Identifiers: – Type: issn-print Value: 00223239 Numbering: – Type: volume Value: 187 – Type: issue Value: 1 Titles: – TitleFull: Journal of Optimization Theory & Applications Type: main |
| ResultId | 1 |