Optimality conditions via a unified direction approach for (approximate) efficiency in multiobjective optimization
Mehrdad Ghaznavi, Fatemeh Akbari, Esmaile Khorram · Optimization methods & software · 2019
The presented paper addresses scalarization techniques for multiobjective optimization problems. A new scalarization technique for solving a general multiobjective optimization problem is proposed. This scalarization method is called the unified direction method, because it generalizes the Pascoletti–Serafini approach (direction approach). Some theoretical results related to the suggested scalarization technique are established, especially the ability of the method for generating (properly, weakly) efficient solutions is shown. Moreover, the relation between approximate optimal solutions of the proposed single objective problem and approximate (weakly, properly) efficient solutions of the multiobjective optimization problem is investigated. In fact, easy-to-check, necessary and sufficient conditions for ϵ-(weak, proper) efficiency are obtained. Moreover, the effectiveness of the proposed approach is illustrated with some illustrative computational examples.