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minimize $-r_1*r_2*...*r_n$
Equation constraint: $x_1^2/r_1^2 +... + x_n^2/r_n^2=1$
m nonlinear inequality constraint : $f_i(x_1,...,x_n) \geq 0$ $i=1,...,m$

I want to find the ellipsoid with maximal volume. The constraints limit the size of the ellipsoid, they are functions with n variable.

user128576
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    Try to type out the problem using MathJax. You'll probably get more responses that way. – Allawonder Aug 07 '19 at 19:15
  • What make you think it is not a valid problem? – user605486 Aug 08 '19 at 03:45
  • A standard optimization problem has decision variables and constraints, which are functions of the decision variables. Here my decision variables are $r_1,..., r_n$, but the constraints are functions of $x_1,...x_n$. So I think I have to get rid of either of those. – user128576 Aug 08 '19 at 07:33

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