Convert the perspective function of log-sum-exp to cvx

(Vicky_Mu) #1

hey every one, I am new to cvx and I am trying to convert this to cvx:

I think it is the perspective function of log-sum-exp, I don’t know how to deal with it in Matlab, can anyone help me with it? Thanks in advance!

(Mark L. Stone) #2

Is t constrained to be >= 0? Presuming it is, you can look at Convert problem to cvx which I think will let you handle (28a) and (28b).

I don’t know the values of your input data, but you have not yet convinced me that (28c) and (28d) are convex. Can you do so? That is your responsibility per the “rules” of the forum.

(Vicky_Mu) #3

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©).
I can also prove (28d) is convex in the same way.

I learned the

Blockquote Convert problem to cvx

but I don’t know how to realize the perspective function of log-sum-exp,
variables x,y,z
{x,y,z} == exponential(1)?
It is just exponential cone but not log-sum-exp, right?

(Mark L. Stone) #4

You are still not providing all the information on the coefficients, variables, or whatever, needed to determine the convexity of (28c) and (28d). If they are convex as you say, you ought to be able to eliminate multiplicative factor of t and use inv_pos to enter those constraints.

As for (28a) and (28b), I was suggesting use of exponential cone to model the individual perspective terms.