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Nonlinear objectives, nonlinear constraints, non-convex objective, non-convex feasible region.
1
vote
Formulating a problem as a mixed-integer conic program
The only option I see is to exploit the fact that $x$ is binary, so in each step of each product you are either multiplying $1$ or $b_i$ on top of what you already had.
If $s,t$ are continuous variabl …
3
votes
Accepted
Linear optimization with one positive definite quadratic equality condition in P?
The following conditions
$$
\begin{array}{l}
y=\sum x_i^2\\
0\leq x_i\leq 1\\
y=\sum x_i
\end{array}
$$
are equivalent to $x_i\in \{0,1\}$, which means your construction allows you to introduce bina …