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.
Mots-clés : ϵ-Efficiency, semi-infinite optimization, ϵ-optimality conditions, ϵ-duality
@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}, publisher = {EDP-Sciences}, volume = {52}, number = {4-5}, year = {2018}, doi = {10.1051/ro/2018028}, mrnumber = {3884161}, zbl = {1411.90327}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ro/2018028/} }
TY - JOUR 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 UR - http://www.numdam.org/articles/10.1051/ro/2018028/ DO - 10.1051/ro/2018028 LA - en ID - RO_2018__52_4-5_1397_0 ER -
%0 Journal Article %A Shitkovskaya, Tatiana %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 %N 4-5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2018028/ %R 10.1051/ro/2018028 %G en %F RO_2018__52_4-5_1397_0
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. http://www.numdam.org/articles/10.1051/ro/2018028/
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