Optimality conditions of robust convex multiobjective optimization via ε-constraint scalarization and image space analysis

In this paper, we investigate robust optimality conditions of convex multiobjective optimization problems with data uncertainty by epsilon-constraint scalarization method and image space analysis. We firstly present the concepts of robust solutions to convex multiobjective optimization problems with data uncertainty. The relationships between robust solutions of uncertain convex multiobjective optimization problem and that of its corresponding epsilon-constraint optimization problem are also obtained. Besides, we employ the image space analysis to establish a theorem of alternative for the epsilon-constraint robust optimization, which allows to get the robust optimality conditions of optimal solutions of the epsilon-constraint robust optimization. Lastly, we establish the sufficient and necessary optimality conditions of the robust efficient solutions for convex multiobjective optimization problems with data uncertainty.