Can CVX solve this kind of function {x-log(1+x/(x+1))}


(TaoChen Lu) #1

My code is as follow:

cvx_begin
variable x;
minimize(x-1000*log(1+0.01*x/(x+1));
subject to
x>0;
cvx_end

Then it reported:

Disciplined convex programming error:
Cannot perform the operation: {real affine} ./ {real affine}

log(1+x/y) is a kind of formation of Information entropy,and my obj function is concave. Is there any ways to rewrite this object function ? Thank you.


Conic formulation for this concave beast involving log?
(Michal Adamaszek) #2

What if you write it as x-1000*log(1.01-0.01*inv_pos((x+1))). I’m not sure this is correct cvx syntax, I just mean transform the expression like this.


(TaoChen Lu) #3

Well,This is a problem. I just don’t know what kind of expression it should be converted into.And x-1000*log(1+0.01*x*inv_pos(x+1)) reported another error:

Cannot perform the operation: {positive constant} ./ {real affine}


(TaoChen Lu) #4

Or I don’t know if it can solve this problem just like this expression


(Michal Adamaszek) #5

All I know is that my expression is equivalent to yours and conic representable. I’m not sure it implies it also works in cvx but if not it should be only a matter of me making a syntax error.


(Mark L. Stone) #6

@Michal_Adamaszek 's solution is correct, and is accepted and solved by CVX.

cvx_begin
variable x
minimize(x-1000*log(1.01-0.01*inv_pos((x+1))))
subject to
x>0
cvx_end

@04014540 Can you show us the complete program you ran which triggered the error message Cannot perform the operation: {positive constant} ./ {real affine} ?


(TaoChen Lu) #7

Sorry,I just found my mistake.@Michal_Adamaszek 's solution is right.Thank you so much and I can use a model that similar to this to solve the problem about Information entropy.Best wish to you.


(TaoChen Lu) #8

Yes,your solution is correct.Thank you!


(Xiaowen Cao) #9

Good afternoon. I have met a relevant about Information entropy question like log(1+1/x)<a. Would you mind send your problem and the corresponding solution to me? It might be a great honor for me to receive your reply. Many thanks!