Yet Another Math Programming Consultant

In this post, I want to discuss indicator constraints and how to replace them with simple multiplications. As we shall see, this is a somewhat harebrained but still interesting idea. 
Indicator constraints are implications of the form: \[\delta=0 \implies \text{linear constraint}\] or \[\delta=1 \implies \text{linear constraint}\] where \(\delta \in \{0,1\}\) is a bina...

In this post, let's do some experiments with the "hostile brothers problem." We have a plot of land. In my test models \([L,U]\times [L,U]\) with \(L=0\), \(U=100\)). We want to place \(n\) brothers on this plot. As they don't get along, we want to spread them out by maximizing the distance between neighbors. In modeling terms, we create a maximin model that maximizes the mini...

Here, I delve into the problem of finding the largest empty rotated square. Given \(n\) data points, find the largest square rotated by an angle \(\theta\), such that the square does not contain any of the points.  In [1], I discussed two special cases: an axis-aligned square (angle is 0°),a diamond shape, which is a square rotated by 45°.Here we focus on arbitrary a...

Finding largest empty shapesThis post is about finding empty regions (square, rectangle, or circle) in a (large) collection of given points. These are interesting little optimization problems.DataI generated \(n=100\) data points \((x_i,y_i), i=1,\dots,n\) drawn from a uniform distribution \[\begin{align}&x_i \sim U(0,10) \\ & y_i \sim U(0,10)\end{align} \] 
It...