So far what I have found in online and in Numerical recipes book describe algorithm for scalar value multi variable function. Can anyone point me to the algorithm for nonlinear conjugate gradient for vector valued ($x_1(u,v)$,$x_1(u,v)$, $x_1(u,v)$....$x_n(u,v)$) function? My cost function is the discrete harmonic function that is widely used in computer graphics: $E = \sum_i \sum_{j,(i,j)\in E} ||v_i - v_j||^2$, each of $v_i$ & $v_j$ has two directions $(u,v)$; $u_i=u_i(u,v), v_i=v_i(u,v)$.
Thanks in advance.