## Tuesday, August 31, 2021

### matrix operations via GAMS Embedded Python: multi-regional Input-Output tables

 Wassily Leontief in front of an IO table, credit:NYU

#### Inverting a dense matrix

GAMS allows running pieces of Python code as part of a GAMS model. Unfortunately, the interface is rather low-level and inefficient.  Usually "low-level" is associated with high-performance, but in the Python world, this is not the case. Here is an example.

## Sunday, August 15, 2021

### Stable Marriage Problem

 An inter-cast marriage ceremony in Lalitpur [6]

The Stable Marriage Problem is a fascinating problem. In this problem, we want to assign ("marry") men to women much like the assignment problem. (I am just following the conventions in the literature here.) There is a twist, however. We want to require that the matchings are stable: there does not exist a combination $$(m,w)$$ such that $$m$$ and $$w$$ both prefer each other above their current partner [1].

There are famous algorithms for this problem [2]. But here, I want to look at it as an integer programming problem.

## Sunday, August 8, 2021

### A network model: Pyomo vs GAMS

Network models are an important class of optimization models, in itself but also as part of larger models. In [1] a nice presentation is given on how to set up a network model in the Python-based modeling tool Pyomo.

The simple shortest path problem is reproduced here: