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

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Minimizing $x_1^2+x_2^2+x_3^2+x_1x_2+x_2x_3+x_3x_1$

The question is about the signature of a quadratic form $$ \sum_{i=1}^n x_i^2 + \frac12\sum_{1 \le \mathrm{dist}(i,j) \le p} x_ix_j $$ (or about the spectrum of the corresponding linear operator). The …
Ivan Izmestiev's user avatar