On optimality conditions and duality theorems for robust semi-infinite multiobjective optimization problems

2016 ◽  
Vol 269 (1-2) ◽  
pp. 419-438 ◽  
Author(s):  
Jae Hyoung Lee ◽  
Gue Myung Lee
Keyword(s):  
Multiobjective Optimization ◽  
Optimality Conditions ◽  
Optimization Problems ◽  
Duality Theorems ◽  
Multiobjective Optimization Problems

scholarly journals Duality Theorems for (ρ,ψ,d)-Quasiinvex Multiobjective Optimization Problems with Interval-Valued Components

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 894
Author(s):  
Savin Treanţă
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Integral Functional ◽  
Multiple Integral ◽  
Control Problems ◽  
Duality Theorems ◽  
New Class ◽  
Duality Results ◽  
Multiobjective Optimization Problems ◽  
Interval Valued

The present paper deals with a duality study associated with a new class of multiobjective optimization problems that include the interval-valued components of the ratio vector. More precisely, by using the new notion of (ρ,ψ,d)-quasiinvexity associated with an interval-valued multiple-integral functional, we formulate and prove weak, strong, and converse duality results for the considered class of variational control problems.

scholarly journals Multiobjective Convex Optimization in Real Banach Space

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2148
Author(s):  
Kin Keung Lai ◽  
Mohd Hassan ◽  
Jitendra Kumar Maurya ◽  
Sanjeev Kumar Singh ◽  
Shashi Kant Mishra
Keyword(s):  
Banach Space ◽  
Multiobjective Optimization ◽  
Saddle Point ◽  
Optimality Conditions ◽  
Pareto Optimality ◽  
Real Banach Space ◽  
Optimization Problems ◽  
Mixed Integer ◽  
Multiobjective Optimization Problems ◽  
Necessary And Sufficient

In this paper, we consider convex multiobjective optimization problems with equality and inequality constraints in real Banach space. We establish saddle point necessary and sufficient Pareto optimality conditions for considered problems under some constraint qualifications. These results are motivated by the symmetric results obtained in the recent article by Cobos Sánchez et al. in 2021 on Pareto optimality for multiobjective optimization problems of continuous linear operators. The discussions in this paper are also related to second order symmetric duality for nonlinear multiobjective mixed integer programs for arbitrary cones due to Mishra and Wang in 2005. Further, we establish Karush–Kuhn–Tucker optimality conditions using saddle point optimality conditions for the differentiable cases and present some examples to illustrate our results. The study in this article can also be seen and extended as symmetric results of necessary and sufficient optimality conditions for vector equilibrium problems on Hadamard manifolds by Ruiz-Garzón et al. in 2019.

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