Questions tagged [linear-programming]

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Two-stage stochastic linear optimization

I am familiar with the notion of two-stage stochastic optimization but I have not found any constructive examples so far, so I am stuck now on how to actually implement this on a given problem. The ...
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33 views

How do get rid of (1 not defined because of singularities) in R? [duplicate]

I'm analyzing data in R, I'm trying to see how some variables affect test scores (Value) of different countries. In the data, since there is different time periods for different countries I need to ...
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1answer
55 views

Defining LP investment model in Lindo/Solver [closed]

Models provided below. My questions are: 1. (G+I+M) after each constraint in the screenshot of the mathematical model below represents Growth, Income and Money ...
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1answer
20 views

Subtract costs from the max profit or factor-in costs into the objective function?

I have the following model with profit being these selling prices for V and C: £3.5V + £5.2C. But there are also costs of V & C which are £1.30 and £1.70 respectively. When I run the model without ...
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0answers
9 views

Total Cost Constrained MDP Python implementation?

I am looking for any Python code that could help me solving Constrained MDP with infinite-horizon. In short I have a problem with two types of costs: A and B, and I want to solve "class" MDP ...
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1answer
108 views

Is it possible to optimize correlation coefficient under linear constraint?

I am new to optimization and recently bump into a problem where I have to optimize the correlation coefficient of a series of values with the absolute value of another vector under the linear ...
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1answer
9 views

Least squares for fitting a line with some thickness?

One can use least squares to fit a line to a set of points. However, these lines lack "thickness". (When I say "thickness", I refer to the orthogonal distance below and above the ...
2
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1answer
30 views

Resulting shapes when partitioning the constraint matrix $\boldsymbol{A}$ in linear programming

\begin{equation} \boldsymbol{A} = \begin{bmatrix} {1}_n^\top \otimes \mathbb{I}_m \\ \mathbb{I}_n \otimes {1}_m^\top \end{bmatrix} \in \mathbb{R}^{(m+n)\times mn} \end{equation} If the above matrix ...
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5answers
1k views

Can we use linear regression to define the objective function in linear programming?

This is a general question about how linear programming is used in the analytics community. Is it common, or feasible to use linear regression (or perhaps even more complex models like regression ...
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0answers
42 views

Formulating a mixed integer programming problem with a binary maximization term

Real-world description of the problem: In the US, funding for school lunch programs is given to local school districts by the Federal government. If >=40% of students in a school or group of schools ...
2
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1answer
25 views

An artist published M albums. How to make a selection from the album so that all my N favorite songs are covered, while minimizing my cost?

This is a real life question.. I have a list of N favorite songs from an artist. Out of all M albums from the artist ever published,I want to buy a few albums to cover all of my N favorite songs, but ...
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0answers
56 views

how to set up an optimization problem to split a group of people into two groups, with several constraints

I am a bit stuck with this problem; I found a temporary (an perhaps suboptimal) solution using Excel, but I'd like to hear your opinion /advice, please. 9 people want to form a group and go on on a ...
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2answers
3k views

Formulating quantile regression as Linear Programming problem?

How do I formulate quantile regression as a Linear Programming problem? When looking at the median quantile problem I know it is \begin{align} \text{minimize } & \sum_{i=1}^n |\beta_0 + X_i \...
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1answer
131 views

Assignment Problem (Linear Programming, Genetic Algorithm, etc.)

I'm looking for advice on how I should approach a specific problem. Some background first: The problem is about shipments falling into a bin. There are 19 such bins, which are further sorted into 20 ...
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0answers
151 views

Linear programming optimization [closed]

I have found through my reading that applying linear programming optimization techniques are substantially more expensive compared to mean squared error-based methods. Could someone please help in ...
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1answer
63 views

If we “delete” the term of norm in SVR problem formulation, can it be solved with simplex method?

The problem formulation in Support Vector Regression is, What if we don't want to take the "flatness" term, i.e., $\frac 1 2 ||w||^2$ and delete it; can we find solution from simplex method for ...
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1answer
76 views

lp_solve starting basis

I'm working with some fairly large LP problems in R and running into very slow computation times. I'm using the 'lp_solve' solver R wrapper ( through lpSolve and lpSolveAPI packages ), and found the ...
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2answers
1k views

How to use equalities as constrains with constrOptim in R

I want to solve a matrix system which have several solutions (infinite since it is overdetermined - 6 equations with 8 unknowns). However, the way I want to do it is to a criterion for the variables, ...
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0answers
39 views

Converting general form to standard form in linear programming

I am new to linear programming and I am currently trying to convert a general LP problem to standard form. The general form the problem is as follows: I have the following objective function, in ...
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0answers
40 views

Is there a method to fit a bound to the plot of an linear inequality?

I have a physical dataset that is bounded by several different processes, and thus the plot takes the form of a linear inequality: I'm specifically interested in studying the upper bound. Is there a ...
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2answers
546 views

Linear programming with variables in piecewise intervals

Problem: I am working on a linear programming problem, i.e. a linear objective function to minimize: $\mathbf{c}\cdot\mathbf{x}$, where $\mathbf{c},\mathbf{x}\in\mathbb{R}^{N}$ Subject to ...
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0answers
1k views

AIC/BIC for quantile regression

I am working on Quantile Regression (QR) and want to assess models using goodness of fit (GOF) measures. I have come across the post here, here that says, AIC/BIC can be calculated for QR model ...
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2answers
4k views

How to solve least absolute deviation by simplex method?

Here is the least absolute deviation problem under concerned: $ \underset{\textbf{w}}{\arg\min} L(w)=\sum_{i=1}^{n}|y_{i}-\textbf{w}^T\textbf{x}|$. I know it can be rearranged as LP problem in ...
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0answers
219 views

Why is Coordinate Descent not used to solve Least Absolute Deviation?

I have recently been looking into why Least Absolute Deviation (LAD) is not used in place of OLS for machine learning, and it appears the primary reason is due to difficulty in computing a solution ...
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1answer
239 views

Does every gutter point in SVM have positive multiplier?

I understand that SVM is about solving the constrained optimization such that $$\min_{\mathbf{w}} \dfrac{1}{2} \mathbf{w}^T\mathbf{w}$$ subject to $$y_i(\mathbf{w}^T\mathbf{x_i}+b)\geq{1}, i=1, 2, ....
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1answer
887 views

Is there a measure to describe the degree of linear separability?

I know that given two sets of points, one can use linear programming to see if there is a solution/hyperplane that linearly separates the two data sets. But this holds for completely linearly ...
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0answers
31 views

Reference for infinite horizon constrained Markov decision process

I am looking for some introductions or reviews material for solving infinite horizon constrained Markov decision process. The book I am reading upon is constrained Markov decision process by Eitan ...
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1answer
21 views

Binary Stochastic Programming with Independent or Positively Correlated Co-efficients

A manufacturer can select a maximum of $N$ stores to fulfill orders from a total of $M$ stores who are looking for inventory, $N\le M$. The case when $N\geq M$ is trivially solved when all stores ...
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0answers
52 views

Looking for canonical problems or seminal work it the intersection of constraint programming and statistics

I'm interested in exploring the area (if it exists) at the intersection of constraint programming and statistics. My primary interest is on problems that require a combination of both statistical and ...
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1answer
105 views

Optimization based on regression result

I am trying to find the optimal values for a given attributes. In particular, my objective is to maximize the profitability based on some parameters. If we call the profitability $p$, and the ...
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2answers
90 views

How to convert minimize $\| Ax - b \|_\infty$ to an equivalent linear program step by step?

Given this question: $$\text{minimize } \| Ax - b \|_\infty$$ Then this question is equivalent to $\text{minimize } \max |Ax - b|$ = $\text{minimize } \max\limits_i |a_i^Tx - b_i|$ Let $t = |a_i^...
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1answer
4k views

How to use MATLAB's Linprog to solve LP model of L1 regression

A L1 regression problem is given as: $\min\limits_{a,b} \sum\limits_{i=1}^n |y_i - ax_i - b|$ It has an equivalent LP model: $\min \sum\limits_{i = 1}^n z_i$ $|y_i - ax_i - b| \leq z_i$ where $...
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1answer
2k views

Linear vs. Quadratic Programming: Complexity and Practical Efficiency

Are quadratic programs harder than linear programs to solve (or vice-versa?) How much harder? I'm interested both in theoretical results and what sort of differences there tend to be in practice.