Consider the quadratic function $f(x_1,x_2,x_3,x_4)=x_1+2x_2+4x_4+x_1^2+5x_2^2+3x_3^2x_4^2-4x_1x_2-2x_2x_3+2x_3x_4$. Is f a convex function?
Consider a constraint defined using the above function f: $f(x_1,x_2,x_3,x_4)\le6$. Is is a convex constraint?
I think f is a convex function when I write the function in matrix notation I have the sum of a positive definite matrix and a linear vector. How do I show that a constraint is convex?