Arcording to this post, smart manipulation of difficult non-linear constraints by a change of variable can lead to a formulation of Geometric Programming.
$\begin{array}{*{20}{c}} {\min }&{\underbrace {{f_0}\left( x \right)}_{{\rm{Posynomial}}}}\\ {s.t}&{\underbrace {{f_i}\left( x \right)}_{{\rm{Posynomial}}} \le 1}\\ {}&{\underbrace {{g_i}\left( x \right)}_{{\rm{Monomial}}} = 1} \end{array}$
In my case, I was having trouble of reformulating the following simple linear constraints into GP constrainst:
$x + y \ge 1$
Does that mean that this simple linear constraint cannot be reformulate as a GP constraints ${\underbrace {{f_i}\left( x \right)}_{{\rm{Posynomial}}} \le 1}$ ?
As a follow up question, I am having a strange gut feeling that although GP has a great expressive power, it cannot be used to express all Linear Programming problem but I am not sure if I am correct on this issue or not?
Edit: In my application I am pretty sure that all of my decision variable x and y are in the interval of [0,1] that is $x,y \in \left[ {0,1} \right]$ . I am not sure if this could help !
Please help me with this,
Thank you for your enthusiasm !
For your particular example $x+y \ge 1$ with $x,y\in[0,1]$, you can introduce $\bar{x}$ to represent $1-x$ and $\bar{y}$ to represent $1-y$. Then your constraint becomes $1-\bar{x}+1-\bar{y} \ge 1$, equivalently, the posynomial constraint $\bar{x}+\bar{y} \le 1$.