Happy new year, I have a function of the form below \begin{align} f(x,y,z)=\sum_i x_i y_i z_i + g(x)+h(z)\cr x,y,z \in R^n \end{align} where $h,g$ are quadratic functions. My difficulty lies in the first term which makes it non-convex.
I read this method of converting a polynomial of any degree to a quadratic function SDP Relaxations for Quadratic Optimization Problems Derived from Polynomial Optimization Problems. But I don't understand what is the moment matrix? and what's the need for it. Because it makes the problem huge and impractical.
Question: How to convert this problem to a quadratic optimization problem with small additional variables and constraints? what is your suggestion to solve such a problem?
Any Hint or suggestions appreciated.