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Optimization and algorithms

I'm going over my practice midterm, and the last question has me stuck. It goes: Let $n \geq 1$ be an integer and let A be a symmetric $n \times n$ matrix (not necessary positive definite) for which ...
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How to properly formulate the objective function and constraints for an ERM linear program in R?

So I am having an issue I tried on my own but it seemed to no avail. It concerns the ERM (Empirical Risk Minimization) algorithm, used in Ban and Rudin's paper for solving a Newsvendor problem, which ...
nhdnhd's user avatar
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What kind of optimization problem is this and what tools can be used to find a solution?

Problem description: The location of n solar panels is defined by the x,y location of the solar panels. Every solar panel must be protected by an anode. Each anode can protect up to 4 solar panels ...
Ryan Conway's user avatar
1 vote
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Including intercept terms in piecewise linear programming

I am hoping to get some help in understanding whether the intercept terms are required in the objective function for piecewise linear programming (using the below code). ...
Marley's user avatar
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1 answer
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How do you optimize multiple objective functions simultaneously?

For example, suppose we want to maximize the 3 expressions on the right, subject to some constraints. To give some context, this is a problem about generating prototypes in unsupervised learning. In ...
Machine Learner's user avatar
2 votes
1 answer
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Combinations from different sets with weightings

Imagine the following scenario: I want to create 1000 unique combinations of clothing. The combinations would include the following categories: hats, shirts, shorts, socks and shoes. Each combination ...
Phima's user avatar
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2 votes
2 answers
325 views

Neural Nework and mathematical programming

I am solving a scheduling problem where staff members cannot have overtime. For this problem, I have an integer programming model and solve it using the CPLEX solver. A simplified version of this ...
mdslt's user avatar
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duel regression with orthogonal constraints on coefficients [closed]

I'm trying to solve a problem where I need to find two deming style regression models onto two different data sets of equal dimension who's coefficients(A,B) satisfy the following criteria with ...
N A's user avatar
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is it possible to estimate least squares model coefficients by linear programming?

I'm not a linear programming expert, I was just wondering; Can I get the same coefficients that I get in the least squares method with a linear programming model whose objective function is minimizing ...
Samet Sökel's user avatar
5 votes
1 answer
72 views

How can we allocate when we have 150 open slots every day (5 days a week) for those 200 arrivals every day

My question is to solve a very basic problem related to the allocation of slots. Say there are 20 teams with 10 persons in each team. I have 150 open slots every day (5 days a week) for those 20 teams ...
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Assigning Objects To Groups Using Variance

I have a set of 1945 objects, each with multiple attributes. They are all stored in a single data.frame named X. For this ...
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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 ...
Omar Perez Rodriguez's user avatar
1 vote
1 answer
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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 ...
Edison's user avatar
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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 ...
Edison's user avatar
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4 votes
1 answer
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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 ...
flashing sweep's user avatar
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1 answer
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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 ...
Captain Crime Bill's user avatar
2 votes
1 answer
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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 ...
develarist's user avatar
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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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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 ...
Adam Rivers's user avatar
3 votes
1 answer
33 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 ...
nobody's user avatar
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2 votes
0 answers
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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 ...
user6376297's user avatar
13 votes
3 answers
6k 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 \...
machazthegamer's user avatar
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1 answer
195 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 ...
Siddharth Mehta's user avatar
2 votes
0 answers
294 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 ...
jeza's user avatar
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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 ...
mah's user avatar
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2 votes
1 answer
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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 ...
jameselmore's user avatar
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2 answers
3k 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, ...
pkpkPPkafa's user avatar
1 vote
0 answers
302 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 ...
Shilpa Kancharla's user avatar
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50 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 ...
Halyn Betchkal's user avatar
1 vote
2 answers
872 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 ...
user2221361's user avatar
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0 answers
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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 ...
Enigma's user avatar
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13 votes
2 answers
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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 ...
southdoor's user avatar
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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 ...
Chris Wood's user avatar
5 votes
1 answer
380 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, ....
Nicholas's user avatar
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8 votes
1 answer
2k 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 ...
Nicholas's user avatar
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1 vote
0 answers
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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 ...
Ping's user avatar
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1 answer
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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 ...
texmex's user avatar
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1 vote
0 answers
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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 ...
1 vote
1 answer
121 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 ...
H_A's user avatar
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1 vote
2 answers
103 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^...
Fraïssé's user avatar
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1 vote
1 answer
5k 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 $...
Fraïssé's user avatar
  • 1,560
1 vote
1 answer
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.
capybaralet's user avatar