Optimality conditions via a unified direction approach for (approximate) efficiency in multiobjective optimization

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 epsilon-(weak, proper) efficiency are obtained. Moreover, the effectiveness of the proposed approach is illustrated with some illustrative computational examples.

Automated summary

The presented paper introduces a new scalarization technique, the unified direction method, for solving multiobjective optimization problems. The paper discusses the theoretical results related to this method, including its ability to generate efficient solutions and its relation to approximate optimal solutions of single objective problems. Furthermore, the effectiveness of the proposed approach is demonstrated through illustrative computational examples.