MHB Finding Vertices of Polyhedron with Simplex Method

  • Thread starter Thread starter evinda
  • Start date Start date
Click For Summary
The discussion focuses on finding the vertices of a polyhedron defined by specific linear equations and constraints using the simplex method. The user initially transforms the variables to ensure positivity, leading to a new set of equations and a matrix representation. They explore different combinations of linearly independent vectors to find basic feasible solutions, ultimately identifying potential solutions while questioning the impact of constraints on the variables. The conversation shifts towards verifying the correctness of the matrices and solutions, with a consensus that checking extreme values under given constraints is crucial for determining the vertices of the polyhedron. The dialogue emphasizes the importance of understanding linear independence and the implications of variable bounds in the context of the simplex method.
  • #31
I like Serena said:
Normally a polyhedron consists of a number of vertices connected by edges, such that faces (polygons) are formed.
A polyhedron usually has a certain volume.
If there are 2 faces or less, it won't contain a volume, and is considered degenerate.
In this case we don't even have a face - only a single line segment. (Nerd)

So in this case we can say that if the line segment is one of the edges of a polyhedron , then its endpoints are vertices of the polyhedron. Right? (Thinking)
 
Physics news on Phys.org
  • #32
evinda said:
So in this case we can say that if the line segment is one of the edges of a polyhedron , then its endpoints are vertices of the polyhedron. Right? (Thinking)

Exactly. (Nod)
 
  • #33
I like Serena said:
Exactly. (Nod)

Nice... Thank you! (Smile)
 

Similar threads

MHB Are all the basic feasible solutions accepted?
  • · Replies 4 ·
Replies
4
Views
2K
MHB How to Determine \( z_k - c_k \) Values in Simplex Method?
  • · Replies 21 ·
Replies
21
Views
4K
MHB Optimal Solution for Linear Programming Problem
  • · Replies 4 ·
Replies
4
Views
2K
I Sampling theory and random sample
  • · Replies 5 ·
Replies
5
Views
2K
B General explicit solution to polynomial interpolation
  • · Replies 3 ·
Replies
3
Views
2K
MHB Relation Algebra - Relational Calculus
  • · Replies 6 ·
Replies
6
Views
1K
MHB Binomial Distribution: Likelihood Ratio Test for Equality of Several Proportions
  • · Replies 1 ·
Replies
1
Views
3K
MHB Solving System of Restrictions with Simplex Algorithm
  • · Replies 25 ·
Replies
25
Views
4K
MHB The column gets out of the basis
  • · Replies 1 ·
Replies
1
Views
1K
MHB Quine-McCluskey method: Prime implicants - disjunctive minimal forms
  • · Replies 3 ·
Replies
3
Views
2K