I have come across a maximisation problem that I do not know how to handle. I have posted the question here in the past.
I have the following function to maximise for $x,y$ $$f(x,y)=a_1 \cos(x) +b_1 \sin(x)+a_2 \cos(y) +b_2 \sin(y)+ a_3 \cos(y-x) +b_3 \sin(y-x)$$
I could not come with an idea for a closed form solution, therefore I am wondering if there is any numerical method for maximising these kind of nonlinear/sine functions. In general, when we have sum of multiple sine functions, is there any numerical method to maximise/minimise them?
P.S. Note that $\cos(\cdot)$ functions are maximised at $x=y=0$ and $\sin(\cdot)$ functions are maximised at $x=y=\pi/2$, therefore the $f(x,y)$ is concave in $0<x,y<\pi/2$ and so itt has a maximum in $0<x,y<\pi/2$.
Any reference/help/hint will be a appreciated