Linear Program Optimal Extreme Points

2022-10-06 Thread Prabhu Manyem
To Andrew, Peter and Manuel, Thank you for your help on this topic. To Manuel, Why only vertices next to the starting vertex? If the links are A-->B-->C and B-->D, so first you go from A to B, then B to C, then backtrack to B (from C), and then you can go from B to D... This is what I had in

Re: [Fwd: Linear Program Optimal Extreme Points]

2022-10-06 Thread Naszvadi Peter
Hi, A finite dimensional polyhedron could have exponentially many vertices! For an all-zero objective function - in case when the LP problem turns to a feasibility problem: no one can check nor list all the vertices in polynomial time = no polynomial size witness, can't be NP-complete! Even

Re: [Fwd: Linear Program Optimal Extreme Points]

2022-10-06 Thread Manuel Muñoz Márquez
Hi, Andrew: I don't kown if it is implemented somewhere. But the problem of generating all the optimal vertices is the same as generating all the vertices of a new polyhedron in 1 lower dimension. But that problem is known to be NP-complete [1], so it is very hard or almost impossible as soon

[Fwd: Linear Program Optimal Extreme Points]

2022-10-06 Thread Andrew Makhorin
Forwarded Message From: Prabhu Manyem To: fuk...@math.ethz.ch, Andrew Makhorin , avis@cs.mcgill.c a Subject: Linear Program Optimal Extreme Points Date: Thu, 6 Oct 2022 10:04:22 +1030 Dear Andrew, Komei, David, I am a retired Maths professor in Adelaide, Australia. About the