The Avriel-Ben-Tal algebraic operations approach for a short version proof of the Karush-Kuhn-Tucker optimality conditions
In this paper, by using (h, ϕ)-generalized directional derivative and (h, ϕ)-generalized gradient, the authors directly derives the Karush- Kuhn-Tucker conditions by applying a corollary of Farkas lemma under the Mangasarian-Fromovitz constraint qualification.Furthermore, the boundedness of Lagrange...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Sciendo
2017-07-01
|
| Series: | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/auom-2017-0019 |
| _version_ | 1811329833070755840 |
|---|---|
| author | Cornaciu Veronica Ioana Ileana |
| author_facet | Cornaciu Veronica Ioana Ileana |
| author_sort | Cornaciu Veronica |
| collection | DOAJ |
| description | In this paper, by using (h, ϕ)-generalized directional derivative and (h, ϕ)-generalized gradient, the authors directly derives the Karush- Kuhn-Tucker conditions by applying a corollary of Farkas lemma under the Mangasarian-Fromovitz constraint qualification.Furthermore, the boundedness of Lagrange multipliers is showed. |
| first_indexed | 2024-04-13T15:50:54Z |
| format | Article |
| id | doaj.art-6913df04ba0043b0a6927b86200e8fb5 |
| institution | Directory Open Access Journal |
| issn | 1844-0835 |
| language | English |
| last_indexed | 2024-04-13T15:50:54Z |
| publishDate | 2017-07-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| spelling | doaj.art-6913df04ba0043b0a6927b86200e8fb52022-12-22T02:40:50ZengSciendoAnalele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica1844-08352017-07-01252394810.1515/auom-2017-0019The Avriel-Ben-Tal algebraic operations approach for a short version proof of the Karush-Kuhn-Tucker optimality conditionsCornaciu Veronica0Ioana Ileana1Doctoral School of Mathematics, University of Bucharest Academiei nr.14, Bucharest, 010014, RomaniaPhD Student, Doctoral School of Mathematics, University of Bucharest, Academiei nr. 14, Bucharest, 010014, RomaniaIn this paper, by using (h, ϕ)-generalized directional derivative and (h, ϕ)-generalized gradient, the authors directly derives the Karush- Kuhn-Tucker conditions by applying a corollary of Farkas lemma under the Mangasarian-Fromovitz constraint qualification.Furthermore, the boundedness of Lagrange multipliers is showed.https://doi.org/10.1515/auom-2017-0019generalized algebraic operationsgeneralized gradientfarkas lemmakarush-kuhn-tucker conditionslagrange multipliersprimary 49k35 |
| spellingShingle | Cornaciu Veronica Ioana Ileana The Avriel-Ben-Tal algebraic operations approach for a short version proof of the Karush-Kuhn-Tucker optimality conditions Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica generalized algebraic operations generalized gradient farkas lemma karush-kuhn-tucker conditions lagrange multipliers primary 49k35 |
| title | The Avriel-Ben-Tal algebraic operations approach for a short version proof of the Karush-Kuhn-Tucker optimality conditions |
| title_full | The Avriel-Ben-Tal algebraic operations approach for a short version proof of the Karush-Kuhn-Tucker optimality conditions |
| title_fullStr | The Avriel-Ben-Tal algebraic operations approach for a short version proof of the Karush-Kuhn-Tucker optimality conditions |
| title_full_unstemmed | The Avriel-Ben-Tal algebraic operations approach for a short version proof of the Karush-Kuhn-Tucker optimality conditions |
| title_short | The Avriel-Ben-Tal algebraic operations approach for a short version proof of the Karush-Kuhn-Tucker optimality conditions |
| title_sort | avriel ben tal algebraic operations approach for a short version proof of the karush kuhn tucker optimality conditions |
| topic | generalized algebraic operations generalized gradient farkas lemma karush-kuhn-tucker conditions lagrange multipliers primary 49k35 |
| url | https://doi.org/10.1515/auom-2017-0019 |
| work_keys_str_mv | AT cornaciuveronica theavrielbentalalgebraicoperationsapproachforashortversionproofofthekarushkuhntuckeroptimalityconditions AT ioanaileana theavrielbentalalgebraicoperationsapproachforashortversionproofofthekarushkuhntuckeroptimalityconditions AT cornaciuveronica avrielbentalalgebraicoperationsapproachforashortversionproofofthekarushkuhntuckeroptimalityconditions AT ioanaileana avrielbentalalgebraicoperationsapproachforashortversionproofofthekarushkuhntuckeroptimalityconditions |