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Linear Programming and LAD Regression
I believe any book on linear programming will mention LAD (Least Absolute Deviation) or \(\ell_1\) regression: minimize the sum of the absolute values of the...
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Linear Programming and Chebyshev Regression
The LAD (Least Absolute Deviation) or \(\ell_1\) regression problem (minimize the sum of the absolute values of the residuals) is often discussed in Linear Programming textbooks: it has a few...
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Integer Programming and Least Median of Squares Regression
Least Median Regression (LMR) [1] is another attempt to make regression more robust, i.e. less sensitive to outliers.\[\begin{align}\min_{\beta}\>&\operatorname*{median}_i r_i^2 \\&y-X\beta...
View ArticleFun with indicator constraints
In [1] a simple model is presented for the Least Median of Squares regression problem:\[\begin{align}\min\>&z\\&\delta_i=1 \Rightarrow \> –z \le r_i \le z\\&\sum_i \delta_i =...
View ArticleUsing Nonlinear Mixed-integer Programming
In [1] we explored some linear mixed-integer programming formulations for the Least Median of Squares regression problem. Now let’s look at some nonlinear formulations.Quadratic modelA mixed-integer...
View ArticleSparse Matrix export from GAMS to R
The problemA colleague posed the question to me: how we can export a GAMS parameter to an R sparse matrix?. A sparse matrix is a matrix where most of the elements are zero. In large scale optimization,...
View ArticleSciPy 1.0 linear programming
The simplex solver in SciPy has been somewhat of a problem. It is a text-book LP solver (tablaux based), so only suited for very small problems. Even on those small problems it is just not very...
View ArticleQuantum Development Kit: Does it come with an LP solver?
Microsoft has released a preview of their Quantum Development Kit [1]. May be we can solve some interesting optimization problems with this [2,3].ReferencesAllison Linn, The future is quantum:...
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Permuted Matrix Balancing
In [1] the following problem is posed:ProblemI am trying to generate a matrix of numbers with 7 rows and 4 columns. Each row must sum to 100 and each column must have an even spread (if permitted)...
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A production scheduling problem
ProblemA post in [1] describes an interesting problem:I have read about cutting stock problem, but this is a bit different.We have orders in different variants, and a maximum sized machine to produce...
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SOS1 variables and Wikipedia
In Wikipedia [1] the following definition of a Special Ordered Set of Type 1 (SOS1) is given:Special Ordered Sets of type 1 (SOS1 or S1): are a set of variables, at most one of which can take a...
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Filling rectangles with polyominos
I know about dominos, but polyominos [1] are new for me. In [2] a problem is posted: fill a rectangle (or square) with a number of different polyominos. No overlap or rotation allowed. I assume there...
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Variant of an Assignment Problem
The standard assignment problem can be stated as:\[\begin{align}\min\>&\sum_{i,j} c_{i,j} x_{i,j}\\ & \sum_j x_{i,j} = 1 && \forall i\\ & \sum_i x_{i,j} = 1 && \forall...
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A difficult row selection problem
The problemIn [1] an interesting problem is posted. From a matrix \(A_{i,j}\) (\(i=1,\dots,m\),\(j=1,\dots,n\)) select \(K\) rows such that a cost function is minimized. Let \(S\) be the set of...
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New book: linear programming using matlab
If you want to know more about the nitty-gritty details of linear programming solvers, this hefty book (637 pages) may be of interest. Contains lots of Matlab code that implement different LP...
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Solving a facility location problem as an MIQCP
Facility location models [1] are one of the most studied areas in optimization. It is still interesting to build a model from scratch.The question is [2]:Given \(m\) customer locations, find the...
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Least squares as QP: convexity issues
In [1] a non-negative least squares problem is solved using Cplex's matlab interface (function cplexlsqnonneglin [2]).Model 1The model this function tries to solve...
View ArticleCBC and semi-continuous variables
CBC does not seem to have a way to specify semi-continuous variables in either an LP file or an MPS file [1] (slightly edited): Hi,I am using version 2.9.9 of cbc in ubuntu 17.10 docker image. My...
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Knuth and SAT
Presentation by Knuth about SAT problems and solvers (and also a little bit about Integer Programming). Not new but still interesting..Section 7.2.2.2 is about SAT. Ran out of extra space for more...
View ArticleLinearizing nested absolute values
In [1] an interesting question is posted: How to model a nested absolute value: \[ \min \left| \left( |x_1-a_1| \right) - \left( |x_2-a_2|\right) \right| \] A standard way to model absolute values in...
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