ε-weak Pareto minimality in D. C. vector optimization
Omar Benslimane, Nazih Abderrazzak Gadhi, Imad Amrani Zerrifi · Numerical Algebra Control and Optimization · 2024
In this note, we consider a vector optimization problem $ \left( P\right) , $ where the objective function and the constraint set are denoted by using differences of two vector-valued mappings, respectively. In order to get sufficient optimality conditions for an $ \varepsilon $-weak Pareto minimal point, we introduce the $ \varepsilon $ -pseudo Diff-Max property which in a weaker version of the Diff-Max property. Using Jeyakumar's alternative theorem dedicated to cone-subconvexlike mappings, we also established necessary optimality conditions. The obtained results are given in terms $ \varepsilon $ -subdifferentials of data-functions. Examples that illustrate our findings are also given.