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Towards optimal experimentation in online systems

The Unofficial Google Data Science Blog

If the relationship of $X$ to $Y$ can be approximated as quadratic (or any polynomial), the objective and constraints as linear in $Y$, then there is a way to express the optimization as a quadratically constrained quadratic program (QCQP). However, joint optimization is possible by increasing both $x_1$ and $x_2$ at the same time.