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I have an optimization problem with linear objective, and constraints that are all linear except for one constraint of the form

$S^2+C^2=1$,

which corresponds to elements in a rotation matrix.

What are effective ways to solve this? I have never tried sequential linear programming, but is that appropriate here?

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If you have a single two-dimensional nonconvex constraint like this (assuming it's not sufficient to relax it to a convex constraint like $ S^2 + C^2 \le 1 $) then I'd recommend simply discretizing the 2d unit ball and solving an LP for each possible value of $(S,C)$.

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