Timeline for Find a matrix and its inverse satisfying lower and upper bounds
Current License: CC BY-SA 3.0
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| Aug 21, 2016 at 0:18 | comment | added | fedja | @Robert Israel Indeed, though the disconnectedness in my example is even more malignant because it can proliferate (just consider the block matrix with $n$ two by two blocks; it will create $2^n$ components each of which can be destroyed by a separate restriction and, therefore, has to be caught by any "sure" algorithm. Thus, the complexity is at least exponential in $n$ :-( ) | |
| Aug 17, 2016 at 21:33 | comment | added | Robert Israel | When the bounds allow it, you may have some solutions with $\det(A) > 0$ and others with $\det(A) < 0$, but of course none with $\det(A)=0$, so again the set of solutions is disconnected. | |
| Aug 17, 2016 at 14:17 | comment | added | fedja | Another thing this example shows is that the set of solutions may be disconnected, which is extremely disconcerting as far as general constraint problems go... | |
| Aug 17, 2016 at 14:03 | history | edited | fedja | CC BY-SA 3.0 |
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| Aug 17, 2016 at 13:51 | history | answered | fedja | CC BY-SA 3.0 |