View in EDS HTML Full Text PDF Full Text

Second-Order Set-Valued Directional Derivatives of the Marginal Map in Parametric Vector Optimization Problems.

Saved in:
Bibliographic Details
Title: Second-Order Set-Valued Directional Derivatives of the Marginal Map in Parametric Vector Optimization Problems.
Authors: Bao, Nguyen Xuan Duy1,2 (AUTHOR) nxdbao@hcmut.edu.vn, Khanh, Phan Quoc3 (AUTHOR) phanquockhanh@tdtu.edu.vn, Tung, Nguyen Minh4 (AUTHOR) tungnm@hub.edu.vn
Source: Journal of Optimization Theory & Applications. Mar2025, Vol. 204 Issue 3, p1-20. 20p.
Subjects: Multi-objective optimization, Directional derivatives, Mathematical mappings, Computational mathematics, Mathematical optimization, Set-valued maps
Abstract: We study second-order differential sensitivity in parametrized vector optimization problems with inclusion constraints. First, we consider a set-valued unconstrained problem and establish a sufficient condition for the second-order directional Dini derivative of the marginal map to be equal to the minimum of that of the objective map. We then extend our research to vector optimization problems with general inclusion constraints and demonstrate that the first- and second-order directional Dini derivatives of the objective image map are equal to the union of those of the objective map. Using advanced proof techniques, we derive a formula for the second-order directional Dini derivative of the marginal map and prove the second-order semi-derivability of the feasible objective and marginal/efficient-value maps. Examples are provided to illustrate the novelty and depth of our results. [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.)
Database: Engineering Source
Full text is not displayed to guests.
FullText Links:
  – Type: pdflink
Text:
  Availability: 1
Header DbId: egs
DbLabel: Engineering Source
An: 182468220
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Second-Order Set-Valued Directional Derivatives of the Marginal Map in Parametric Vector Optimization Problems.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Bao%2C+Nguyen+Xuan+Duy%22">Bao, Nguyen Xuan Duy</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> nxdbao@hcmut.edu.vn</i><br /><searchLink fieldCode="AR" term="%22Khanh%2C+Phan+Quoc%22">Khanh, Phan Quoc</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> phanquockhanh@tdtu.edu.vn</i><br /><searchLink fieldCode="AR" term="%22Tung%2C+Nguyen+Minh%22">Tung, Nguyen Minh</searchLink><relatesTo>4</relatesTo> (AUTHOR)<i> tungnm@hub.edu.vn</i>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22Journal+of+Optimization+Theory+%26+Applications%22">Journal of Optimization Theory & Applications</searchLink>. Mar2025, Vol. 204 Issue 3, p1-20. 20p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Multi-objective+optimization%22">Multi-objective optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Directional+derivatives%22">Directional derivatives</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+mappings%22">Mathematical mappings</searchLink><br /><searchLink fieldCode="DE" term="%22Computational+mathematics%22">Computational mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Set-valued+maps%22">Set-valued maps</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: We study second-order differential sensitivity in parametrized vector optimization problems with inclusion constraints. First, we consider a set-valued unconstrained problem and establish a sufficient condition for the second-order directional Dini derivative of the marginal map to be equal to the minimum of that of the objective map. We then extend our research to vector optimization problems with general inclusion constraints and demonstrate that the first- and second-order directional Dini derivatives of the objective image map are equal to the union of those of the objective map. Using advanced proof techniques, we derive a formula for the second-order directional Dini derivative of the marginal map and prove the second-order semi-derivability of the feasible objective and marginal/efficient-value maps. Examples are provided to illustrate the novelty and depth of our results. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  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=egs&AN=182468220
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1007/s10957-025-02606-7
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 20
        StartPage: 1
    Subjects:
      – SubjectFull: Multi-objective optimization
        Type: general
      – SubjectFull: Directional derivatives
        Type: general
      – SubjectFull: Mathematical mappings
        Type: general
      – SubjectFull: Computational mathematics
        Type: general
      – SubjectFull: Mathematical optimization
        Type: general
      – SubjectFull: Set-valued maps
        Type: general
    Titles:
      – TitleFull: Second-Order Set-Valued Directional Derivatives of the Marginal Map in Parametric Vector Optimization Problems.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Bao, Nguyen Xuan Duy
      – PersonEntity:
          Name:
            NameFull: Khanh, Phan Quoc
      – PersonEntity:
          Name:
            NameFull: Tung, Nguyen Minh
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 03
              Text: Mar2025
              Type: published
              Y: 2025
          Identifiers:
            – Type: issn-print
              Value: 00223239
          Numbering:
            – Type: volume
              Value: 204
            – Type: issue
              Value: 3
          Titles:
            – TitleFull: Journal of Optimization Theory & Applications
              Type: main
ResultId 1