Timeline for Bounding distance to a polyhedron
Current License: CC BY-SA 4.0
2 events
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| Feb 9 at 11:45 | comment | added | Igor Khavkine | In general you may need to keep $n\ge m$ hyperplanes $H_i$ at a given vertex, but with any $m$ of the $v_i$ linearly independent. The worst will happen for $x$ along the rays generated by the vertices of the polyhedron $(x,v_i) \le 1$ (choosing the right signs for the $v_i$), that is, where for $m$ of the hyperplanes $(x,v_i) = 1$. So a sharper constant is $C = \max_I \| A_I^{-1} d \|$, where $d=(1,\ldots,1)$ and $A_I$ is the submatrix of $A$ with $m$ rows indexed by $I \subseteq \{1, \ldots, n\}$. One should also of course maximize this $C$ over all vertices of $P$. | |
| Feb 8 at 22:26 | history | answered | Anton Kapustin | CC BY-SA 4.0 |