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On the Mangasarian–Fromovitz constraint qualification and Karush–Kuhn–Tucker conditions in nonsmooth semi-infinite multiobjective programming

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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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Acknowledgements

This work was supported by Vietnam National University-Hochiminh City under the Grant B2018-28-02. A part of the work was completed during a stay of the authors at the Vietnam Institute for Advanced Study in Mathematics (VIASM). The authors would like to thank VIASM for its hospitality and support. They are grateful to the anonymous referees for their very helpful remarks and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, International University, Ho Chi Minh City, Vietnam

    Phan Quoc Khanh

  2. Vietnam National University, Ho Chi Minh City, Vietnam

    Phan Quoc Khanh & Nguyen Minh Tung

  3. Department of Mathematics and Computing, University of Science, Ho Chi Minh City, Vietnam

    Nguyen Minh Tung

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  1. Phan Quoc Khanh
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  2. Nguyen Minh Tung
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Correspondence to Nguyen Minh Tung.

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Khanh, P.Q., Tung, N.M. On the Mangasarian–Fromovitz constraint qualification and Karush–Kuhn–Tucker conditions in nonsmooth semi-infinite multiobjective programming. Optim Lett 14, 2055–2072 (2020). https://doi.org/10.1007/s11590-019-01529-3

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