Simultaneous equation models and data errors

My experience is that using (optimization) models is a great way to provide quality assurance on the data. Data collection can be very difficult and expensive. It can also be quite easy to have errors cropping up somewhere along the way. When using an optimization model, we will get hammered by such errors.

Algorithm vs. model

From [1]:

We are given a plane defined by Ax+By+Cz-D = 0 where D is significantly larger than A,B,C and GCD(A,B,C) = 1. How would I find all points (x, y, z), where x,y,z are integers and >= 0, that lie on the plane in an efficient manner?

So the poster asks for an algorithm to find \(\color{darkred}x,\color{darkred}y,\color{darkred}z \in \{0,1,2,\dots\}\) such that \[\color{darkblue}A \cdot \color{darkred}x + \color{darkblue}B \cdot \color{darkred}y + \color{darkblue}C \cdot \color{darkred}z = \color{darkblue}D\] Besides the assumptions stated in the question, I'll further assume \(\color{darkblue}A,\color{darkblue}B,\color{darkblue}C,\color{darkblue}D\gt 0\).

Choosing between NLP solvers: interior point or active set.

One way to categorize (local) nonlinear programming (NLP) solvers is active set methods and interior point solvers. Some representative large-scale sparse solvers are:

• Active set: CONOPT, SNOPT. These are using SQP algorithms.
• Interior point: IPOPT, Knitro. Note: Knitro also contains an active set algorithm.

These are two very different types of algorithms. They work very well on different types of problems. If you do a lot of nonlinear optimization, it actually makes sense to have both types of solvers available. With modeling tools like AMPL and GAMS, it is very easy to switch between solvers. Testing performance between two solvers is then also a snap.

Here I want to discuss some factors that can help in deciding whether to use an active set solver or an interior point solver. 

Some approaches for moving data between MS Access and GAMS

Moving data between different environments is always more difficult than we hope. Here I list some approaches and actually try them out on a small dataset. We hit some bugs along the way and also a few conceptual stumbling blocks (even for this stylized example). We had some issues with Access as well as GAMS Connect. 

This question came up in an actual project. My idea was: "Let me show you how this can be done". I am afraid, I got carried away a bit. But it demonstrates that we should not underestimate these, at first sight, menial tasks. When the data set becomes larger, the problems compound. We can't eyeball the data, and statistically, it is more likely we encounter some problems.