The important part is proving that: convex convex. Trivially, the set is convex as well.
S is convex, meaning for all and any we have .
Now, for you to prove that is convex, prove that any convex combination .
I need to prove the following but I am struggling to see where to start:
The image of a convex set under an affine transformation i.e. the set for , where
However, I know how to prove convex.
Thanks in advance,
Thank you for your answer! I ended with this below as proof ... does it make sense to you?
Proof: . Now to prove that is convex, I need to prove that any convex combination
Let and . Then applying the Convex definition:
Finally by convex definition where convex and then is convex too.
I am not a mathematician but interested to learn the course Convex Optimization ... a bit too many proofs for a poor programmer like me