Nonlinear objectives, nonlinear constraints, non-convex objective, non-convex feasible region.

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### Nonlinear matrix equation 2

Solve the following nonlinear equations for $v$ and $w$
$Avv^TAw+Bvv^TBw=\lambda_1v+\lambda_2w$
$Aww^TAv+Bww^TBv=\lambda_1w+\lambda_2v$
$v^Tw=w^Tv=0$
$v^Tv=w^Tw=1$
where $\lambda_1, \lambda_2, ...

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### Does Quadratic Programming get easier when it's described by a diagonal matrix?

Generally, Quadratic Programming solves the problem
$$\text{Given }Q, c, A, b,\text{ choose }x \text{ to maximize } x^TQx + c^Tx \text{ subject to } Ax \le b$$
In this form, Quadratic Programming is ...

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### product of variables in objective function

Hi there,
I'm looking for a solver that allows me to solve an optimization problem of the form min x1*x2*x3,...,xn subject to some linear constraints. I've used gurobi before, however I couldn't find ...