# Questions tagged [linear-programming]

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

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### Using absolute error as the cost function

This is related to my previous post Minimize distance between curves. I have a dataset with values of multiple curves. An example plot is shown below. I want to scale the curves (move up/down) so that ...
70 views

### How can we model time progress in linear programming?

I am trying to solve a scheduling problem with linear programming. I have N disks that each have a capacity of constant C. At each time interval t_i, a set of write requests with different sizes ...
61 views

### Linearize problem with absolute value

Is there any method to linearize the following optimization problem? \begin{align} min_{x,y} &~~ c~[x; y] \\ st &~~ \sum x\leq \alpha_1 \\ &~~ \sum |y|\leq \alpha_2 \\ &~~ \sum y= 0 \\ ...
329 views

### Python solvers for MINLP in Pyomo in Google Colab

I am looking for a MINLP solver that works with Pyomo models which can be used in the Google Colab environment. I have already found MindtPy but it doesn't work in google colab.
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### Equivalence between zero sum games and linear program

It is well known that you can use the algorithm for finding the equilibrium of a Zero-sum game to solve a linear program. In particular, you can take a LP and reduce it to a zero-sum game, and use the ...
71 views

### Maximum Constraints Satisfaction of Linear Programming

The question I need to solve is to maximize the satisfied constraints in linear programming. To be more specific, Suppose I have an infeasible LP problem, my goal now, is to find the maximum number of ...
56 views

### Model and solve nutrition optimization problem: how to?

How to solve/assess the following problem? Given: $N$ ingredients like apples, bread etc. Mass of an ingredient $j$ is in this simplified model a sum of macro nutrients carbohydrates, proteins and ...
209 views

### Symmetric matrix which satisfies conditions of the form $v_i^T X v_i = 0$

I want to solve an underdetermined system of linear equations $A x = b$ with $A \in \mathbb{R}^{n \times r^2}, x \in \mathbb{R}^{r^2}, b \in \mathbb{R}^n$. The matrix $A$ has the following additional ...
51 views

### Balanced constraint

In several optimization problems, we found what we called the balanced constraint(c^T • x = z ) For exp: C^T • 1 = 0 (C is a binary Matrix) Can I have an intuitive explanation about the concept and ...
1 vote
172 views

### Linear system with an l1-norm constraint

I have a saddle-point system of the form \begin{equation} \begin{bmatrix} A & B \\ B^T & O \end{bmatrix}\begin{bmatrix} x\\ y \end{bmatrix} = \begin{bmatrix} f \\ \vec{0} \end{bmatrix}, \end{...
1 vote
263 views

### Solving a linear program with an active set method

Is it possible to solve a linear program with an active set method? If so what would be the similarities and differences to the simplex method?
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### Using MILP to place a set of primers along a genome

Define variables $p_i,u_i\in\{0,1\}^G$, for $i=1,\ldots,8$ and $G=30000$. Let $v$ be a constant vector also in $\{0,1\}^G$, with approximately 25% of its entries equal to $1$ (randomly located). Let ...
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### Optimizing vectors with equal elements

I am trying to distribute power across different devices, so that the sum is as equal as possible to the power setpoint. At the same time, the sum of power per phase must not exceed the power of the ...
1 vote
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### Fastest way to solve linear programming with 6 complex inequalities and 5 nonnegative variables

I have a program where I need to solve a linear programming problem in a fast loop. The language I'm using is Java and any kind of bindings to other languages are not acceptable. Libraries might be ...
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### Why do active set methods or the simplex method pivot only one variable at a time?

Why do active set methods or the simplex method pivot only one variable at a time? Ostensibly, we could add multiple columns to the basis during pivoting, but the standard presentation of the methods ...
1 vote
2k views

### Solve a set of multivariate linear inequalities with constraints in Python

I'm trying to implement Dinur-Nissim algorithm and am stuck at how to solve the set of linear inequalities with multiple unknowns and a large number of equations along with constraints. Example: \...
835 views

### How to perform linear programming sensitivity analysis in MATLAB?

I would like to perform post-optimal analysis using Matlab linprog. But it does not provide any information about that. So required a way to get the info about optimal basis, basic and non-basic ...
62 views

### Linear programming with stochasticity?

Suppose I have implemented an LP, where some constraint coefficients are implemented as the mean of some probability distribution. Now, I would like to solve the same problem but with stochasticity ...
1 vote
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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 ...
Is there any sufficient and necessary condition to check the feasibility of the linear constraints $Ax=b, x\geq 0$ without solving an LP with a constant objective function? $x$ is the variable and \$...