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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; 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
@article{RO_2018__52_4-5_1397_0,
     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},
     year = {2018},
     publisher = {EDP-Sciences},
     volume = {52},
     number = {4-5},
     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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AU  - Shitkovskaya, Tatiana
AU  - Kim, Do Sang
TI  - ϵ-Efficient solutions in semi-infinite multiobjective optimization
JO  - RAIRO - Operations Research - Recherche Opérationnelle
PY  - 2018
SP  - 1397
EP  - 1410
VL  - 52
IS  - 4-5
PB  - EDP-Sciences
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%A Kim, Do Sang
%T ϵ-Efficient solutions in semi-infinite multiobjective optimization
%J RAIRO - Operations Research - Recherche Opérationnelle
%D 2018
%P 1397-1410
%V 52
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%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/ro/2018028/
%R 10.1051/ro/2018028
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