Nonnegative Generalized Inverses and Interval Linear Programs

Abstract

Connections between nonnegative generalized inverses and interval linear programs form the subject matter of this article. Characterizations of nonnegativity of the Moore–Penrose inverse and the group inverse are presented and their role in the study of a special class of optimization spaces, namely, Ben-Israel–Charnes spaces is brought out. The interplay between Ben-Israel–Charnes spaces and other notions of generalized inverse positivity are also studied.

Keywords:

• Ben-Israel–Charnes space
• Interval linear program
• Nonnegative group inverses
• Nonnegative Moore–Penrose inverses
• Weak monotonicity

AMS Subject Classification:

• 47B60
• 47B65
• 15A09
• 90C48

ACKNOWLEDGMENTS

The author acknowledges Professor M. Z. Nashed and the anonymous referee for their critical comments that has improved the manuscript. Part of the work was carried out when the author was affiliated to the Chennai Mathematical Institute. The author acknowledges the Chennai Mathematical Institute for providing necessary facilities and the National Board for Higher Mathematics, Government of India, for financial support.