How to reformulate the log function as its equivalent conic programming?

[Abbas Omidi]

Dear support team,

I hope you are doing well. I am trying to solve an optimization problem that contains power functions. The problem is something like this:

Max_(x,y) = (y/x)

s.t:   

5**(x) =e= 5*x

2**(y) + 8**(y) =e= 130

(x,y) in R

I reformulated the problem via a logarithmic function, and it works well. Now, I would like to reformulate the mentioned problem as its equivalent conic programming. Also, I want to know if there is a way to reformulate the problem by a general non-linear form (log(x) = y). I was wondering if, how I can rewrite the problem in its conic form, if it is possible?

Best regards

Abbas

[Erling D. Andersen]

Given you have nonlinear equalities then there is no hope you can formulate it on conic form.

The reason is that a nonlinear equality can never specify a convex set.

Erling D. Andersen

MOSEK APS 

Fruebjergvej 3, 

Symbion Science Park Box 16, 

DK-2100 Copenhagen O

Ph: +45 7174 9373

Mo: +45 2362 9520

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[Abbas Omidi]

Dear Dr. Andersen,

Thank you so much for your informative comments.

Best regards

Abbas