As the Optimization Decision Table shows, fmincon is the correct solver to use for this problem. As the documentation shows, you should put your parameters A, B, C, and D into a vector x, so
A = x(1);
B = x(2);
C = x(3);
D = x(4);
Write your nonlinear inequality constraints in the form specified in Nonlinear Constraints. For a simple example, see this example.
Alan Weiss
MATLAB mathematical toolbox documentation