jeffgerickson / algorithms

Bug-tracking for Jeff's algorithms book, notes, etc.
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[Oops.] Problem 1 chapter I #237

Open josiahblaisdell opened 3 years ago

josiahblaisdell commented 3 years ago

Please verify that the error is present in the most recent revision before reporting.

Chapter number or note title: [ "Linear Programming Algorithms" ] (Chapter I) Page number: [12]

Error description: [error] Problem 1 as it is currently written is false unless somehow non-degeneracy somehow implies that the feasible region is bounded. It is not clear to me that this implication works with the definition of non-degeneracy given:

non-degenerate linear programs, in which (a) the objective vector is not normal to any constraint hyperplane, and (b) at most d constraint hyperplanes pass through any point. (pg 14 chapter H)

(a) and (b) seem to hold when the feasible region is unbounded

Suggested fix (if any): [fix] Reword the problem to read "with a bounded feasible region" or possibly reword non-degenerate to exclude the case where the feasible region is unbounded.

or perhaps I am wrong, I think I have a solution to this problem but I cannot tell how to use non-degeneracy to exclude the unbounded feasible region.