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

Abstract

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.

Keywords:

• Multiobjective optimization
• proper efficiency
• scalarization
• unified direction method
• approximate efficient solution

Mathematics Subject Classification (2010):

• 90C29
• 90C30

Acknowledgements

The authors would like to express their gratitude to the handling editor and anonymous referees for their helpful comments and suggestions that improved the quality of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The author M. Ghaznavi would like to acknowledge the financial support of Shahrood University of Technology for this research under project no: 23099.