In Convex Optimization by Stephen Boyd Chapter 3 page 110:
“Many of the results for convex functions have extensions to K-convex functions. As a simple example, a function is K-convex if and only if its restriction to any line in its domain is K-convex.”
Question: Should it not be:
“Many of the results for convex functions..... if and only if its restriction to any K-convex line in its domain is K-convex.”
Because just saying any line may violate the proper cone condition. Since every line Segment inside the cone, not necessarily satisfies the generalized inequality induced by proper cone.
Or what I am failing to understand?