Timeline for Convex hull of the Stiefel manifold with non-negativity constraints
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Jun 9, 2018 at 20:39 | comment | added | Mark L. Stone | $$\mathrm{conv}(\mathrm{St}(n,k) \cap \mathbb{R}^{n\times k}_+) = \{X\in\mathbb{R}^{n\times k}_+:\|X\|_2 \le 1, \Sigma_{j=1}^n X_{ij} \ge 1\ \forall i\}$$ is conjecture (low confidence). However, I am very confident based on semidefinite optimization results that the RHS of that implies all the following claims made in the post., even though I haven't proved those claims. I can state quite confidently that my conjectured convex hull is convex - do you have a way to try to test whether it is correct for some 1 < k < n cases? Maybe @Arian can give it a try? | |
| Jun 9, 2018 at 20:15 | comment | added | Mahdi - Free Palestine | Thanks, Mark. that conjecture can be a constructive progress in solving the problem. | |
| Jun 6, 2018 at 3:24 | history | edited | Mark L. Stone | CC BY-SA 4.0 |
added 81 characters in body
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| Jun 6, 2018 at 2:56 | history | edited | Mark L. Stone | CC BY-SA 4.0 |
Added the additional information that $\sqrt{\frac{k}{n}} \le \|X\|_2$
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| Jun 5, 2018 at 12:14 | history | answered | Mark L. Stone | CC BY-SA 4.0 |