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Questions tagged [simplex]

For questions on the $n$-simplex, an $n$-dimensional polytope with $n+1$ points.

A Simplex is a higher dimensional analogue of a triangle or tetrahedron. It represents the simplest possible polytope made with line segments in any given dimension. The number of faces in a simplex can be determined using Pascal's triangle.

Below is an image of Simplex's of the first, second, third, and fourth dimensions from Wikipedia:

enter image description here

Reference:

803 questions
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Cartesian coordinates for vertices of a regular 16-simplex?

I am using amoeba to solve an optimization problem and want to distribute the initial perturbations uniformly about the initial estimate. With only Excel at my disposal, I cannot figure out how to compute the Cartesian coordinates for the vertices…
EBlake
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Simplex method| Degenerate Dictionary

Suppose that a linear programming problem has the following property: its initial dictionary is not degenerate and, when solved by the simplex method, there is never a tie for the choice of the leaving variable. (a) Can such a problem have…
hans-t
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Singular complex as a $\Delta$-complex model

I'm trying to understand singular complexes via Hatcher page 108. Here is my understanding so far and where I'm not getting it. Given a space $X$, a singular n-simplex is just a $\sigma \in C^1(\Delta^n, X)$ and the boundary maps are linear maps…
roundsquare
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Simplex method: initial tableau from a given feasible solution

I have a linear program that I want to solve using the Simplex Method. I would like help figuring out how to initialize the tableau from a given feasible solution. I have found many instructions how to initialize the tableau generally. But they all…
Guut Boy
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What is the optimal solution

I am trying to maximize my objective function $$3x_1+5x_2$$ subject to \begin{align} x_1+2x_2&\leq5\\ x_1&\leq3\\ x_2&\leq2\end{align} where $$x_1,x_2 \geq0 $$ so this is what I did \begin{align} x_3&=5-x_1-2x_1…
Goodbye World
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dissecting a hypercube to simplexes

I read that an n-cube (hypercube) can be dissected into $n!$ n-simplexes. In case of 2D, I can see that a square can be dissected into two 2-simplexes (traingles). Incase of cube, how we can fit six, tetrahedron inside it ?
Shew
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Geometry of leaving variable in simplex method

Why can't a leaving variable in a simplex method iteration be the entering variable in the next iteration, in terms of the geometry?
hans-t
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Simplex coefficients approaching infinity

So I'm writing an implementation of the simplex algorithm which takes in about 20000 constraints. It seems to run fine, but I'm having this annoying error where after about 5000 pivots, the coefficients on the variables approach infinity and my…
Avi Rudich
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problem with the simplex method

I wrote a pc program that implements the simples method. In most cases, the program output is correct. But there are cases where an error occurs. For example: max -x-y s.t. x<=230 y<=230 x=1 y=0 The problem is converted to: max…
Ido Ikar
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Simplex Algorithm - Constraint for a Basic Feasible Solution

I was watching the lecture videos on Discrete Optimization on Coursera and I came across something I couldn't understand. A solution is feasible if the following constraints (picture below) are satisfied. I have been wondering if it possible for…
Kong
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Complicated situation in the simplex method?

I am having a problem with the simplex method and here is my tableau section $$\begin{array}{|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|} \hline x1 & x2 & x3 & x4 & x5 & x6 & x7 & s1 & s2 & s3 & s4 & s5 & s6 & s7 & s8 & s9 &…
Tuong Nguyen Minh
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Beginner Simplex problem

Good evening, I have started studying the simplex method for some examinations I would like to take, and to be perfectly honest, I am stuck really bad. The basic examples and exercises are simple, and I can generally solve them without problem. But…
Spyros
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Looking for a bijective function mapping an n-simplex to itself

As part of a research question I am exploring, I need to find a bijective function on an n-simplex that maps the midpoint of each sub-simplex to itself. This includes all vertices, midpoints of edges, midpoints of faces, etc. The function should…
Jack
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Can you describe a $3$-simplex in $\mathbb{R}^3$?

I suppose that the standard $3$-simplex must be defined in $\mathbb{R}^4$ because you need four independientes unit vectors. But, since a $n$-simplex is generate by $n+1$ affinely independient points $p_0,\dots,p_n$, I think that in $\mathbb{R}^3$…
user183002
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Simplex method in matrix form with the big $M$ method?

If I have one constraint $3_{x1}+2_{x2}=18$ in a maximize problem you need to fulfil $AX\le b$ what should I do to fit the condition ? What I think is: $3_{x1}+2_{x2}\le 18$ and $3_{x1}+2_{x2}\ge 18$ becomes $-3_{x1}-2_{x2}\le -18.$ In tableau…
Linear Algebra fans
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