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.
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:
(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.