# can we use a hybrid optimization schem for NMF

The NMF problem of the form

$$X \simeq WH$$

is a constrained biconvex optimization problem, and is often solved by alternating updates schemes. For example, the multiplicative update rules use analytic solutions to update the two variables $$\textbf{W, H}$$ alternatively.

\begin{align} For \quad & i=1...niter \\ & Update \quad W\\ & Update \quad H \end{align}

My equation is: can we use a hybrid optimization scheme instead. For example, for $$W$$ we choose a multiplicative update rule and for $$H$$ we choose a projected gradient descent method ?