[Math] How to solve nonlinear constrained optimization in Matlab

Question

I have to solve a nonlinear constrained function in matlab, and I am not familiar with it's commands.
the problem is:
minimize $E(b,c)$
constraints: $k1< c\sqrt{b}< k2 ; c/6>k3$
Note: E(b,c) is a nonlinear function.

Also how can I solve this easier one
minimize $E(b,c)$
constraints: $c \sqrt{b} =k2;c/6>k3$
for simplicity imagine: i.e. $E(b,c)=b^{2}+ \sqrt{c}+c$ and $k1=8,k2=12,k3=5$
I must use Matlab mfile. Please suggest me what should I do!
I would like to plot the $E(b,c)$ based on given constraints and find the $b,c$ pairs, if that is possible.
I am not sure if I really need optimization toolbox or not.
Please give me a short Matlab script if it's ok.
thanks in advance

Answer 1

You can also consider to use the external library Yalmip.