matlabconvex-optimizationcvx

why is Convex function <= Concave function a valid cvx constraint?

I am studying using CVX on MATLAB and encountering this problem that why is the following constraint: Convex function <= Concave function a valid CVX constraint?

Solution

  • Basically because if f is concave, then -f is convex. So say we have:

    f(x) <= g(x)      with f convex, and g concave

    then that means

    f(x)-g(x) <= 0    f-g is convex