Optimality, scalarization and duality in linear vector semi-infinite programming

Abstract

In this paper, we introduce some qualification conditions for a linear vector semi-infinite programming problem. The new qualification conditions are used for development of necessary conditions for weak efficient, isolated efficient and -efficient solutions of such a problem. Sufficient conditions for the existence of such solutions are also provided. In addition, a new general scalarization technique for solving the reference problem is presented. Finally, we propose a type of Wolf dual problem and examine weakstrong duality relations.

Keywords:

• Multiple objective programming
• linear programming
• semi-infinite optimization
• optimality condition
• constraint qualification

Acknowledgements

The authors are grateful to professor Miguel Ángel Goberna for his many helpful suggestions which have improved the presentation of the paper. Also, we would like to thank the anonymous referees for carefully reading our work and for their helpful comments.

Notes

No potential conflict of interest was reported by the authors.

1 Maintain the proof.