A note on second-order Karush–Kuhn–Tucker necessary optimality conditions for smooth vector optimization problems
RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 2, pp. 567-575.

The aim of this note is to present some second-order Karush–Kuhn–Tucker necessary optimality conditions for vector optimization problems, which modify the incorrect result in ((10), Thm. 3.2).

Reçu le :
Accepté le :
DOI : 10.1051/ro/2017026
Classification : 90C29, 90C46, 49K30
Mots clés : Second-order regularity conditions, second-order Karush–Kuhn–Tucker optimality conditions, efficient solution, geoffrion properly efficient solution
Kim, Do Sang 1 ; Tuyen, Nguyen Van 1

1
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     author = {Kim, Do Sang and Tuyen, Nguyen Van},
     title = {A note on second-order {Karush{\textendash}Kuhn{\textendash}Tucker} necessary optimality conditions for smooth vector optimization problems},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {567--575},
     publisher = {EDP-Sciences},
     volume = {52},
     number = {2},
     year = {2018},
     doi = {10.1051/ro/2017026},
     mrnumber = {3880545},
     zbl = {1401.90207},
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     url = {http://archive.numdam.org/articles/10.1051/ro/2017026/}
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Kim, Do Sang; Tuyen, Nguyen Van. A note on second-order Karush–Kuhn–Tucker necessary optimality conditions for smooth vector optimization problems. RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 2, pp. 567-575. doi : 10.1051/ro/2017026. http://archive.numdam.org/articles/10.1051/ro/2017026/

[1] G. Bigi and M. Castellani, Second order optimality conditions for differentiable multiobjective problems. RAIRO: OR 34 (2000) 411–426 | DOI | Numdam | MR | Zbl

[2] G. Bigi and M. Castellani, Uniqueness of KKT multipliers in multiobjective optimization. Appl. Math. Lett. 17 (2004) 1285–1290. | MR | Zbl

[3] R.S. Burachik and M.M. Rizvi, On weak and strong Kuhn-Tucker conditions for smooth multiobjective optimization. J. Optim. Theory Appl. 155 (2012) 477–491 | DOI | MR | Zbl

[4] G. Giorgi, B. Jiménez and V. Novo, Strong Kuhn-Tucker conditions and constraint qualifications in locally Lipschitz multiobjective optimization problem. Top. 17 (2009) 288–304 | DOI | MR | Zbl

[5] M. Golestani and S. Nobakhtian, Nonsmooth multiobjective programming: strong KuhnTucker conditions. Positivity 17 (2013) 711–732 | DOI | MR | Zbl

[6] T. Maeda, Constraint qualification in multiobjective optimization problems: differentiable case. J. Optim. Theory Appl. 80 (1994) 483–500 | DOI | MR | Zbl

[7] T. Maeda, Second-order conditions for efficiency in nonsmooth multiobjective optimization. J. Optim. Theory Appl. 122 (2004) 521–538 | DOI | MR | Zbl

[8] O.L. Mangasarian, Nonlinear Programming. McGraw-Hill, New York (1969) | Zbl

[9] V. Preda and I. Chiţescu, On constraint qualification in multiobjective optimization problems: semidifferentiable case. J. Optimiz. Theory Appl. 100 (1999) 417–433 | DOI | Zbl

[10] M.M. Rizvi and M. Nasser, New second-order optimality conditions in multiobjective optimization problems: differentiable case. J. Indian Inst. Sci. 86 (2006) 279–286 | Zbl

[11] S. Wang, Second order necessary and sufficient conditions in multiobjective programming. Numer. Funct. Anal. Optim. 12 (1991) 237–252 | DOI | Zbl

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