From Boyd & Vandenberghe's Convex Optimization:
where Fig 2.25 is:
I have two questions (First para makes sense to me):
- Q1: The first line of second para describes what it means for $x$ to be minimal. I am confused what is $K$ here? It seems that for second para we are not referring to the set S (as set S is clearly not convex), but I am confused how K (a cone) is chosen when we talk about a set S?
- Q2: For the second para, how come we can say that: From the first inequality we conclude $\lambda \succeq_{K_*} 0$?