Talk:Simplex algorithm

message: I am not sure of this mathematical statement in the overview. 
"It can also be shown that, if an extreme point is not a maximum point of the objective function, then there is an edge containing the point so that the objective function is strictly increasing on the edge moving away from the point."
Since degeneracy can cause a stalling effect, it is possible to find a descent direction where the objective value is not increased, but is still a valid direction. Thus, I doubt the term "strictly", and I don't know how it would need to be phrased since it is only an overview of the algorithm. On another note, do we say that the objective value is increased, or objective function? Raphaelbwiki (talk) 22:33, 26 January 2021 (UTC)
replies: text: You're right! Stalling does not affect the geometric point of view of the statement, thus it is correct. Marking this thread as resolved. Raphaelbwiki (talk) 13:43, 18 June 2021 (UTC)
thread_title:  Simplex overview verification 

message: In this 2011 edit (https://en.wikipedia.org/w/index.php?title=Simplex_algorithm&type=revision&diff=420535791&oldid=420516031), user Kiefer.Wolfowitz (, not active as of April 2021) introduced the statement "Another approach to studying typical phenoma uses Baire category theory from general topology, and to show that (topologically) "most" matrices can be solved by the simplex algorithm in a polynomial number of steps."  This statement has been questioned on cstheory.stackexchange.com here: https://cstheory.stackexchange.com/questions/48850/using-baire-category-to-analyze-the-efficiency-of-the-simplex-method , with no clarification as of April 2021.  From a quick google scholar search, I don't find any research mentioning (much less explaining) anything about the Simplex algorithm and Baire Category theory (except a 2015 online article that appears to be plagiarized from the Wikipedia page).  I suggest that either a suitable reference be found and added, or, if none can be found, that the statement be removed. Nealeyoung (talk) 01:36, 29 April 2021 (UTC)
replies: text: Agreed. I am quite familiar with the literature on analysis of the simplex method, and nothing I have seen outside of this article makes any mention of Baire category theory. Shuiberts (talk) 11:43, 29 April 2021 (UTC)
thread_title:  Reference needed for statement about Baire Category 

message: The example of the pivot operation states:
"Columns 2, 3, and 4 can be selected as pivot columns, for this example column 4 is selected. The values of z resulting from the choice of rows 2 and 3 as pivot rows are 10/1 = 10 and 15/3 = 5 respectively. Of these the minimum is 5, so row 3 must be the pivot row."
The earlier statement on the pivot operation reads:
"The row containing this element is multiplied by its reciprocal to change this element to 1.."
But in the example after the pivot, the value at row 3, column 4 is 3, not 1. 
Hyphz (talk) 19:15, 1 November 2021 (UTC)
replies: text: It seems that all of the elements of the tableau have been scaled by three without saying. This appears to have been done to coerce it as a canonical form. The example could write a big \frac{1}{3} to the left of the tableau and indicate this has been done. An alternative could be to put a denominator of 3 below all of the elements, but that wouldn't look great. I was quite confused by this example. As I am new to wikipedia and linear programming I don't feel confident making an edit until I'm absolutely sure of what I'm doing. Phebenet (talk) 23:47, 23 October 2023 (UTC)
thread_title:  Confusing example