Hi everyone,
I have a following problem. There is a book called
Primal-dual interior-point methods

written by Stephen Wright, available at this link:

Primal-dual interior-point methods - Google Knihy

My problem is to show the converse of theorem 2.3 from this book. Mr. Wright is talking only about the implication A => B, and at the end of his proof, he states that B => A holds as well. I've tried everything, including some attempts with Farkas lemma and other theorems of the alternative, but got stuck. Any ideas for B => A?