I've got an unconstrained optimization problem, and all function involved can be regarded as differentiable as you like.

The variable is a rectangular matrix $M$. Target Function is $\sum_i f(w^i) +\sum_j g(w_j)$, where $w^i,w_j$ corresponds to the i-th row and j-th column of $M$

Is there any preferable methods to solve such problems?

Any thoughts would be helpful. Thanks in advance!