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I don't know what "close to" really means, so let's suppose that you simply did obtain the optimal solution $\vec{x}$. In the generic situation, the objective $f(\vec{x})$ is a unique linear combinat …

The relaxed quadratic programming problem is a red herring. It is true that quadratic programming over $\mathbb{R}$ with linear inequalities can be solved in practice, for one reason because it is a …

I'm not sure about names for this equation. As for solving it, I can say this much: It is a linear system and there is a solution in which $X$ is also symmetric. Following basics of matrix differen …

Certainly if you're given the combinatorial type of the Steiner tree, you can efficiently find its position. The length of each edge is a convex function of the positions of the internal vertices of …

If I understand correctly, we can make a change of variables from $z$ in the upper half plane to $\zeta$ in the unit disk. Then the function $N(\zeta)$ is continuous on the unit circle $\zeta = \exp( …

To elaborate on the comments of Will Sawin and fedja: The question isn't a sorting problem, but it is a matching problem. If $S$ is your arbitrary set and $G = [n]^2$ is your grid, then you are marr …