# Questions tagged [linear-programming]

Questions on linear programming, the optimization of a linear function subject to linear constraints.

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### linear program-Simplex method-Dual problem

At an exercise I am asked to solve a linear program using the simplex method(in Matlab).Then I have to formulate the dual of this problem and read off an optimal solution of the dual problem from the ...
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### Simplex Algorithm

I'm currently trying to implement the (revised) Simplex Algorithm, but according to my notes the LP in standard form $\left( Ax = b, x \geq 0 \right)$ with $A \in \mathbb R^{m \times n}$ has to have ...
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### How to check if steepest gradient method will converge?

So I have this function $f(x,y) = x^4 - 2x^2 +x + 4y^2$ and I want to know if the steepest gradient method will converge if I pick an arbitrary point and apply said method. My initial thought ...
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### How to check linear independence

How can I check the linear independence of my variables? I have this system $Ax=b$ where $A$ is a $N \times 4$ matrix. I want to check the linear independence between the 4 variables in matrix $A$.
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### String satisfying the condition

Given $N$, $A_0$, $B_0$, $L_0$, $A_1$, $B_1$ and $L_1$, find a sequence S consisting only of characters '$0$' and '$1$'(a total of N characters) such that: The number of '$0$'s in any consecutive ...
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### Inequality Constrained Optimization Problem

I am working on the question displayed below. I am not sure if I understand it correctly and I am looking for some input. So, I am asked Why is $x^*$ a local maximum for $f$ subject to the set of ...
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### have value of variable take on whether two other variables equal?

I'm having a hard time expressing something in a linear program I am writing. I have two variables a and b. I want the ...
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### Linear optimization problem

$\mathbf{Problem}$: Varying amount of goods have to be transported along three paths: A,B,C; 780, 2425, 1000 units respectively. Three trucks are available: 1.5, 3.5 and 5 tonne capacity. First two ...
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### Dictionaries which share Basis, are they the same?

I am (trying) to understand the following theorem: If the simplex method does not terminate, it must cycle Now I know that two dictionaries with the same $\mathcal{B}$ have to be encountered ...
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### Show using duality that exactly one of the following systems has a solution

(I) $Ax=b$ ; $0≤ x ≤e$ (II) $uA +v ≥0 ; ub + ve = -1 ; v ≥ 0$
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### Bounded and Feasible of Linear Program?

I have a question on usage of terminology in Linear programming. Why do we have terms like "If an LP is bounded and feasible, then..." My confusion is, if a Linear program is bounded then it has to ...
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### linear equations with inequality constraints

The problem is, given a set of linear equations $Ax=b$ such that the system is under-determined, and a set of linear inequalities $Cx\geq 0$, find a solution for the system. Does anyone know a general ...