The necessary and sufficient conditions for efficient solutions and duality results to Multi-objective optimization problems and their applications to Robust Multi-objective Optimization problems
1.1 We give necessary and sufficient conditions to obtain KKT type optimality results for weakly efficient solutions for (MOP).
1.2 We give necessary and sufficient conditions to obtain KKT type optimality results for properly efficient solutions for (MOP).
1.3 We give necessary and sufficient conditions to obtain KKT type optimality results for efficient solutions for (MOP).
1.4 We will give an example showing that the Slater condition are essential in the Fritz-John type sufficient condition.
1.5 We apply the obtained results to give necessary and sufficient conditions for robust efficient solution, weakly robust efficient solution and properly robust efficient solution for nonsmooth robust multiobjective convex optimiza- tion problems.
1.6 We give an example to illustrate the significance of such results can be ap- plicable in situations while the aforecited results do not work.
