Hi guys,

I met a problem while using cvx. My objective function is f(x,y) = x*log(1+x/y),x>0,y>0. The function is convex, but I don’t know how to express which in cvx. Can you help me?

Thanks

# Writing x*log(1+x/y)

**ramin_hhh**(John) #1

Log(1+1/x) convex function of x. How to implement in CVX fitting DCP rule?

**Mark_L_Stone**(Mark L. Stone) #2

I believe `x*log(1+x/y)`

is convex for x > 0, y > 0.

I don’t see how to get it into CVX. Perhaps someone else knows how, although I don’t know whether it can be done.

As has been posted on this forum, the “similar” looking `x*log(1+y/x)`

can be expressed as `-rel_entr(x,x+y)`

, and is concave for x > 0, y > 0. But I don’t see how to use rel_entr for `x*log(1+x/y)`

Perspective of log det function, and CVX formulations of related log det problems using Quantum Relative Entropy from CVXQUAD

**Michal_Adamaszek**(Michal Adamaszek) #3

`x*log(1+x/y)=rel_entr(x+y,y)+rel_entr(y,x+y)`

**Mark_L_Stone**(Mark L. Stone) #5

@Michal_Adamaszek Nice solution. Nice cancellation of terms. Thanks.

**zhang**(zhangQK) #6

Hi, Mark.

I have a function that is z=0.005*abs(y)*exp(14.4*abs(y)/x) and x>100,-3<=y<=3.And I do not know how to express it in cvx.

Could you help me?

Thank you.

**zhang**(zhangQK) #8

I am sorry,Erling.

But I seem not to ask the question.And I do need to ask to help for this question.

**zhang**(zhangQK) #10

Yes,Erling.

z=0.005*abs(y) *exp(14.4* abs(y)/x) and x>100,-3<=y<=3.

And this function is convex(I have proved).But I do not how to express it so that cvx can accept it.

Thank you.

**zhang**(zhangQK) #11

I am sorry.I omitted a word ‘before’ in my last reply.I mean, I haven’t asked such a question before.