Conic Scalarization Method in Multiobjective Optimization and Relations with Other Scalarization Methods

2015 ◽  
pp. 319-329 ◽  
Author(s):  
Refail Kasimbeyli ◽  
Zehra Kamisli Ozturk ◽  
Nergiz Kasimbeyli ◽  
Gulcin Dinc Yalcin ◽  
Banu Icmen
Keyword(s):  
Multiobjective Optimization ◽  
Scalarization Methods ◽  
Scalarization Method ◽  
Conic Scalarization ◽  
Conic Scalarization Method

Comparison of Some Scalarization Methods in Multiobjective Optimization

2017 ◽  
Vol 42 (5) ◽  
pp. 1875-1905 ◽  
Author(s):  
Refail Kasimbeyli ◽  
Zehra Kamisli Ozturk ◽  
Nergiz Kasimbeyli ◽  
Gulcin Dinc Yalcin ◽  
Banu Icmen Erdem
Keyword(s):  
Multiobjective Optimization ◽  
Scalarization Methods

ϵ-Efficient solutions in semi-infinite multiobjective optimization

2018 ◽  
Vol 52 (4-5) ◽  
pp. 1397-1410
Author(s):  
Tatiana Shitkovskaya ◽  
Do Sang Kim
Keyword(s):  
Multiobjective Optimization ◽  
Nonsmooth Analysis ◽  
Constraint Qualification ◽  
Dual Problem ◽  
Optimization Problems ◽  
Efficient Solutions ◽  
Duality Theorems ◽  
Multiobjective Optimization Problems ◽  
Special Cases ◽  
Scalarization Method

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.

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