On the Mangasarian–Fromovitz constraint qualification and Karush–Kuhn–Tucker conditions in nonsmooth semi-infinite multiobjective programming
We discuss constraint qualifications in Karush–Kuhn–Tucker multiplier rules in nonsmooth semi-infinite multiobjective programming. A version of the Manganarian–Fromovitz constraint qualification is proposed, in terms of the Michel–Penot directional derivative and the Studniarski derivative of order...
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| Vydáno v: | Optimization letters Ročník 14; číslo 8; s. 2055 - 2072 |
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01.11.2020
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| ISSN: | 1862-4472, 1862-4480 |
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| Abstract | We discuss constraint qualifications in Karush–Kuhn–Tucker multiplier rules in nonsmooth semi-infinite multiobjective programming. A version of the Manganarian–Fromovitz constraint qualification is proposed, in terms of the Michel–Penot directional derivative and the Studniarski derivative of order
p
which is just the order of the directional Hölder metric subregularity which is included also in this proposed qualification version. Using this qualification together with the Pshenichnyi–Levitin–Valadire property, we establish Karush–Kuhn–Tucker optimality conditions for Borwein-proper and firm solutions. We also compare in detail our qualification version with other usually-employed constraint qualifications. Applications to semi-infinite multiobjective fractional problems and minimax problems are provided. |
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| AbstractList | We discuss constraint qualifications in Karush–Kuhn–Tucker multiplier rules in nonsmooth semi-infinite multiobjective programming. A version of the Manganarian–Fromovitz constraint qualification is proposed, in terms of the Michel–Penot directional derivative and the Studniarski derivative of order
p
which is just the order of the directional Hölder metric subregularity which is included also in this proposed qualification version. Using this qualification together with the Pshenichnyi–Levitin–Valadire property, we establish Karush–Kuhn–Tucker optimality conditions for Borwein-proper and firm solutions. We also compare in detail our qualification version with other usually-employed constraint qualifications. Applications to semi-infinite multiobjective fractional problems and minimax problems are provided. |
| Author | Khanh, Phan Quoc Tung, Nguyen Minh |
| Author_xml | – sequence: 1 givenname: Phan Quoc surname: Khanh fullname: Khanh, Phan Quoc organization: Department of Mathematics, International University, Vietnam National University – sequence: 2 givenname: Nguyen Minh surname: Tung fullname: Tung, Nguyen Minh email: nmtung@hcmus.edu.vn organization: Vietnam National University, Department of Mathematics and Computing, University of Science |
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| Keywords | Optimality condition Directional Hölder metric subregularity Constraint qualification Firm solution Semi-infinite multiobjective programming Proper solution |
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