linearization of power function

GAMS
1

Hi,
I am facing problem in linearizing the below non-separable function. Any suggestions for linearization of the con_1 ??

Best Regards,
Rofice

variable
c ;
positive Variable
x,y;
integer variable
z;

equation
con_1,con_2;

con_1… x =e= y**z;
con_2… c =e= 3*x ;

y.up = 3;
z.lo = 1;
z.up = 4;

model m /all/
solve m maximizing c using mip;

2

I think you should linearize the 4 possibilities and then using a binary variable to select one.
four possibilities: y^1 (linear) y^2 (non linear and convex) y^3 (non linear and convex) and y^4 (non linear and convex)
bye