Asymptotic optimality conditions for linear semi-infinite programming

Abstract

In this paper, the classical KKT, complementarity and Lagrangian saddle-point conditions are generalized to obtain equivalent conditions characterizing the optimality of a feasible solution to a general linear semi-infinite programming problem without constraint qualifications. The method of this paper differs from the usual convex analysis methods and its main idea is rooted in some fundamental properties of linear programming.

Keywords:

• linear semi-infinite programming
• inclusive cone
• inclusive region
• optimality condition

AMS Subject Classifications:

• MSC 90C34
• MSC 90C46
• MSC 90C22
• MSC 90C25

Acknowledgements

The authors of this paper would like to thank the anonymous referees for their valuable and much appreciated comments and suggestions which helped to improve the quality of the paper.

Notes

No potential conflict of interest was reported by the authors.