# Questions tagged [linear-programming]

Referring to optimization problems that consist only of linear constraints and a linear objective function.

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### Hit-n-Run Monte Carlo on convex polytope

So, I'm currently trying to implement a MCMC to uniformly sampling hyper-points from the polytope defined as $\mathbb{K}=\{x\in\mathbb{R}^{n}\;\;\text{s.t.}\;\; A\,x=b \}$ in the specific case where, ...
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### Long AMPL model preparation time

We deal with a large-scale linear optimization problem (~50000 variables and ~4000000 constraints). We use AMPL Studio modeling environment for problem modeling and then calling linear solver (CPLEX, ...
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### Getting Extremal Rays of Cone

So I have a set of linear homogeneous equations $A\vec{x}=0$. I would like to solve this for non-negative solutions. I can solve the system in general and I get the two vectors that span the solution ...
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### Is it more efficient to capture many constraints in one constraint?

I have a number of variables that need to be set to 0. They are positive real numbers so the way I see it I can do this by setting each one to 0 by separate constraints, or I can set their sum to zero....
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### Largest hypercuboid inside a polyhedron

Given a polyhedron $\mathbf{Ax} \leq \mathbf{b}$, how to find the largest hypercuboid, with unknown center $\mathbf{x_{0}}$ and side lengths $2\epsilon_{i}$, which are aligned along the co-ordinate ...
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### Checking the feasibility of a system of inequalities

I have $m$ inequalities involving $n$ variables as follows $$a_{1,j} x_1 +a_{2,j} x_2 +\dots +a_{n,j} x_n>0 \quad \text{for} \quad 1 \leq j \leq m$$ How can I check if a solution exists (with the ...
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### Generate discrete set of points in a feasible region

I have two vectors which specify the bounds $x_{min}$ and $x_{max}$ of the sample space. Also, it has to satisfy the linear constraint $Ax \leq b$. How to generate an evenly spaced set of points, ...
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### Precision of ratio constraint in a linear program [closed]

I am trying to solve a LP in which one of my constraints is of the form $$\frac{A(x)}{B(x)} = 1$$ I transform this constraint into a linear one $$A(x) - B(x) = 0$$ However when CPLEX solves the ...
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### Literature on comparing Simplex and Interior-Point-Methods (or combining both of them)

Do you know some interesting literature concerning the comparison of Simplex and Interior-Point-Methods referring to linear optimization? I also read about the possibility of combining both of them ...
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### Can Variance be replaced by absolute value in this optimization problem

Initially I modeled my objective function as $$\arg \min \operatorname{Var}(f(x),g(x)) + \operatorname{Var}(c(x),d(x)) + \cdots$$ where $f$, $g$, $c$, $x$ are linear functions. To be able to solve ...
I have the following LP:  \begin{array}{ll} \text{Minimize} & \sum_{j=1}^n x_j \\ \text{Subject to} & \sum_{j=1}^n a_{ij} x_j \geq b_i,~~~i\in\{1,\ldots,M\} \\ & 0 \leq ...