Dear Mark,
Thanks for your answer. Yes, t>=0. And I can prove (28c) is convex since 2^(x)-2^(y) is convex(x>=0 and y>=0), which can be proved by its Hermitian matrix. So its perspective function is also convex (just as 28(c)).
I can also prove (28d) is convex in the same way.
I learned the
Blockquote Convert problem to cvx - #2 by Mark_L_Stone
but I don’t know how to realize the perspective function of log-sum-exp,
like
variables x,y,z
{x,y,z} == exponential(1)?
It is just exponential cone but not log-sum-exp, right?