Geodesic
ϵ-Efficient solutions in semi-infinite multiobjective optimization
RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 4-5, pp. 1397-1410

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In this paper we apply some tools of nonsmooth analysis and scalarization method due to Chankong–Haimes to find ϵ-efficient solutions of semi-infinite multiobjective optimization problems (MP). We establish ϵ-optimality conditions of Karush–Kuhn–Tucker (KKT) type under Farkas–Minkowski (FM) constraint qualification by using ϵ-subdifferential concept. In addition we propose mixed type dual problem (including dual problems of Wolfe and Mond–Weir types as special cases) for ϵ-efficient solutions and investigate relationship between mentioned (MP) and its dual problem as well as establish several ϵ-duality theorems.

DOI : 10.1051/ro/2018028
Classification : 90C30, 49N15, 90C46, 90C34
Keywords: ϵ-Efficiency, semi-infinite optimization, ϵ-optimality conditions, ϵ-duality

Shitkovskaya, Tatiana 1 ; Kim, Do Sang 1

1 
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     author = {Shitkovskaya, Tatiana and Kim, Do Sang},
     title = {\ensuremath{\epsilon}-Efficient solutions in semi-infinite multiobjective optimization},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {1397--1410},
     publisher = {EDP-Sciences},
     volume = {52},
     number = {4-5},
     year = {2018},
     doi = {10.1051/ro/2018028},
     mrnumber = {3884161},
     zbl = {1411.90327},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ro/2018028/}
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Shitkovskaya, Tatiana; Kim, Do Sang. ϵ-Efficient solutions in semi-infinite multiobjective optimization. RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 4-5, pp. 1397-1410. doi: 10.1051/ro/2018028

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