Hi everyone, the image is attached.
Both p(x,y) and q(x,y) are probability density functions, q(x,y) is an already known density function, my job is to minimise C[p,q] with respect to 3 conditions, they are listed in the red numbers, 1, 2, 3. Setting up the lagrange function and simplifying it up to equation (21) is fine with me, however I am lost when they mention "calculus of variations" as I have not studied, I assume (22) follows on from the calculus of variation technique they used, I was wondering where I can read about calculus of variations to help me solve problems like this with integral constraints? Thanks!