Questions tagged [simplex-method]

Question 1

I am a network engineer currently studying optimization problems. Out of curiosity, I was fascinated by the fact that the Simplex Method has an exponential worst-case complexity, a property famously ...

Question 2

In section $3.1$ of Introduction to Linear Optimization from Bertsimas and Dimitris, there's this figure given (represented in the image below) given as an example to illustrate that if a basic ...

Question 3

Context I'm studying linear programming and trying to understand when different solution methods are most appropriate. I understand that the simplex method is generally better than vertex enumeration ...

Question 4

I encountered an implementation of simplex method where the initial basic feasible solution is found by a heuristic rule as follows: The procedure starts with a standard form with slack variables $\...

Question 5

I learned that the Simplex Algorithm can loop forever/return a suboptimal solution whenever it's degenerate. For $n$ variables and $m$ constraints, this is when two or more sets of $n$ constraints are ...

Question 6

I was reading about the Klee-Minty cubes. First of all, I am not sure if there is a typo, namely, that the constraints should be $$2^Dx_1 +\dots + 2^1x_D + 2^0x_D \le 5^D$$ instead of $$2^Dx_1 + \dots ...

Question 7

stackexchange community, I'm learning about optimization and got myself familiar with the Simplex method with Phase I and Phase II. I came across the following exercise: Check with the Simplex method,...

Question 8

Suppose we want to find the minimal value of objective function $c^Tx$ (1) subject to constraints: $a_1^Tx \geq b_1$ $a_2^Tx \geq b_2$ ... $a_m^Tx \geq b_m$ now, for any $y_1,...,y_m$, via weak ...

Question 9

I have an M-problem in linear programming, and I am given the final simplex tableau. In the header row of the tableau, the coefficients of the variables in the objective function are listed. Since all ...

Question 10

I’m on an MSc Data Science course and have recently learned the Simplex method, and have been doing some revision questions to boost my understanding ahead of an exam. One of the revision questions I ...

Question 11

I am studying the cycling of simplex method. I know that there is a lexicographic rule to prevent looping of the simplex method, and I also know that this rule should be applied to a lexicographically ...

Question 12

Bounded-variable simplex method's algorithm From $\textit{'Linear and Nonlinear Optimization'}\ $ by Igor Griva; Stephen G. Nash ; Ariela Sofer; p.219 I'm not sure how $x_2$ is chosen as the entering ...

Question 13

I have given a 4x4 system of the form $Ax = 0, x \geq 0$. I am interested in understanding under which conditions this system has a non-trivial solution. Starting with $Ax=0$ it is a known result that ...

Question 14

I am working through the equivalence of each step of the two algorithms. Wagner's 1957 "A COMPARISON OF THE ORIGINAL AND REVISED SIMPLEX METHODS" states that they are rigorously the same (...

Question 15

First off, I know that both are equivalent up to slack variables. I used to think that the canonical form had the constraint as $Ax = b$, and the standard form had them as $Ax \leq b$ (this is for ...

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Questions tagged [simplex-method]

Does the Interior Point Method Solve Klee-Minty Cubes adversarial instances in Polynomial Time?

How come this example given in my book leave the feasible set in either of the sides of a certain direction ? Analytically it seems it is impossible

Is vertex enumeration preferable to the simplex method in linear programming for finding all basic feasible solutions?

Prove or disprove a heuristic rule to find an initial basic feasible solution in LP

Am I understanding degeneracy in Simplex correctly?

How to come up with Klee-Minty cubes?

Correct way of setting up for Phase I of the simplex method

Why is there a linear combination of the constraints that equals the objective function?

Recovering the Original M-Problem from the Final Simplex Tableau

How would you find unknown values within a given final Simplex tableau for a solved LP problem?

Cycling of Lexicographic simplex method

Bounded-variable simplex method

Under which conditions does the system $Ax=0, x \geq 0$ have a non-trivial solution?

Equivalence between revised simplex and tableau simplex

Does the standard form of a linear program have inequality or equality constrtains?

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