Can symbolic tool box transfer max(f(x), y) into symbolic variable?

I was using fmincon for nonlinear optimization, but When I tried to use MATLAB symbolic toolbox to provide joccobian of my constraint function, MATLAB showed terminated saying the symbolic toolbox cannot transfer function max(f(x), 0). In my constraint function, I called a function handle, and in that function there is max(f(x), 0). I used max(f(x), 0) in order to increase the robustness of my code, otherwise there is a high chance that MATLAB will terminate due to the complex number generated by my constraint function, which is wrong. I have no idea how to deal with the problem between symbolic toolbox and max(f(x),0), if anyone of you have solution I would be very grateful.

Answer 1

[Walter Roberson]

I suggest experimenting with a piecewise(), which you can generate inside the symbolic engine by using

min0 = evalin(symengine, 'x -> piecewise(x<0, 0, x)');

then min0(f(x)).

If that doesn't work, then Heaviside it:

syms min0(x)
min0(x) = x*Heaviside(x);

then min0(f(x))

[Tao]

Thank you Walter, I tried the Heaviside function, and it works but too slow. Since in my main file which I run fmincon, I need to change a variable value in both my objective and constraint function, which means every time I have to recalculate the symbolic gradient and Jaccobian once this variable value is changed. Could you give me any suggestion how to avoid calculating symbolic radient and Jaccobian every time?

[Walter Roberson]

I already answered that in your earlier question http://uk.mathworks.com/matlabcentral/answers/218576-how-to-pass-extra-parameter-as-a-symbolic-variable-to-objective-and-constraint-functions