From Fundamentals of Convex Analysis by Lemerechal and Hiriart-Urrut:
"polarity generalizes orthogonality in a unilateral way"
"convex analysis is the unilateral realm of inequalities, in contrast with linear analysis"
"Moving to the unilateral world of convex analysis, we replace linear hulls by conical hulls, and equalities by inequalities"
The book has mentioned this a couple times and it feels like some deep point about convex analysis but he has never actually explained what "unilateral" means.
Any ideas?