Yes, MATLAB can solve nonlinear optimization problems. Since it would be a lot to type everything out, this example nonlinear constrained minimization should take you step by step through the process.
The gist of the matter is that you will need to create a file that contains your nonlinear constraints - it will look something like this:
function [cin, ceq] = nlcon(x)
a = 2;
b = 2*a;
cin = 1 - 1/(1-exp(x(1)-x(2)+a)) + 1/(1-exp(x(2)-x(1)+b));
ceq = [];
