Brian Kernighan talks about modeling languages

 

Nov 17, 2015 Professor Brian Kernighan presents on 'How to succeed in language design without really trying.' Brian Kernighan is Professor of Computer Science at Princeton University and Honorary Professor in the School of Computer Science at The University of Nottingham.

Basically, Kernighan says:

• GAMS is terrible (somewhat of a side note). This makes some sense: that opinion was probably the reason to develop AMPL in the first place (if he thought GAMS was terrific, why develop AMPL).
• Original declarative AMPL i.e. the part he worked on: good.
• Later procedural facilities in AMPL (he was not involved in that): bad. (IMHO practical modeling often needs some procedural support; this is one of the reasons why modeling tools embedded in Python are popular).

Micro-econometrics: discrete choice models

In this post, I want to discuss some statistical models from [1]. I'll implement these models in GAMS. First of all to emphasize these are all (nonlinear) optimization problems. Instead of using canned routines using a statistical package, this can help to get a better understanding of what is really going on. At least for me, not using a black-box routine, forces me to understand the underlying optimization models. Another application can be to have this part of a larger GAMS model. Some mathematical programming models just need some estimation code before the real model can be attacked. If the rest of the model is in GAMS, it may be a little bit easier to also use GAMS in the estimation tasks, instead of using a statistical package. This actually happens quite a lot. Finally, it may be easier to add constraints using a GAMS formulation compared to a canned routine in a statistical package.

In this case, the first argument was the reason for using GAMS. Reproducing results is for me a good tool to help me understand a dense text.  

Select points

In [1], the following problem is posted:

I have multiple sets of data points. For example, set 1 contains 5 data points, set 2 contains 1 data point, set 3 contains 10, etc. I need to select one data point from each set so that distances between these selected points is minimal. Any Python based functions to be used will be very helpful

This can be stated as an optimization problem. Writing down the model is a useful exercise, not only to solve it and get solutions but also to define the problem a bit more precisely than a typical "word problem". 

A super simple non-convex MIQP model is:

Non-convex MIQP Model
\[\begin{align}\min&\sum_{i,j|\color{darkblue}{\mathit{ok}}_{i,j}} \color{darkblue}{\mathit{dist}}_{i,j}\cdot\color{darkred}x_i \cdot\color{darkred}x_j \\ & \sum_{i|\color{darkblue}{\mathit{group}}_{i,g}} \color{darkred}x_i = 1 && \forall g\\ & \color{darkred}x_i \in \{0,1\} \end{align}\]