Given the equations $||x||_2=1$, $\sum_{i=1}^n x_iy_i=0$ and some of the $y_i$ values sum to zero, e.g., $y_5+y_3+y_2=0$ is it possible to prove that the set $$\mathcal{Y} = \{ y~|~ ||x||_2=1, \sum_{i=1}^n x_iy_i=0, \sum_{i\in\{5,3,2\}}y_i=0\}$$ is convex?
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What is $x$? Is it given? – daw Feb 04 '20 at 07:52
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@daw $x$ is fixed vector with $||x||=1$. – Thoth Feb 04 '20 at 10:32
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In this case, $\mathcal Y$ is even a linear subspace. – daw Feb 04 '20 at 10:48
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@daw if we relax the constraint to $||x||\leq 1$ will that help to prove that $\mathcal{Y}$ is convex? – Thoth Feb 04 '20 at 13:20