I am trying to solve the following minimization problem \begin{equation*} \begin{aligned} & \underset{x,y}{\text{minimize}} & & H(x,y) \\ & \text{subject to} & & f(x,y) \leq \lambda \end{aligned} \end{equation*}
where $H = ||t -\sum_k x_{k}f(y_{k}) - \sum_k x_{k}y_{k}||_2^2$ is smooth, non-convex function and $f = |\sum_k x_{k}f(y_{k})|$ is non-smooth, non-convex function, but it is convex if we keep one variable constant. I was thinking of using Proximal Alternating Linearized Minimization, is this a valid approach? Is there any other approach to solve the above problem? A related problem is Proximal operator of multiplication of two variables