# Chapter 14Applications of mathematical programming

Mathematical programming is, in my view, satisfaction of constraints with an attempt to minimize or maximize an objective function. That is, there are “many” constraints and they are the first focus of our attention. Moreover, the subject has been driven by a number of practical-resource-assignment problems, so the variables may also be integers instead of or as well as real numbers.

## 14.1 Statistical applications of math programming

In this field, R shows its statistical heritage and is not at the forefront. Most statisticians do not use math programming. I include myself in this. My needs for such tools have largely been driven by approximation problems where we wish to minimize the sum of absolute errors or the maximum absolute error. There are also situations where I have wanted to solve some optimization problems such as the diet problem, where the constraints are the required total intake of nutrients or limits on salt and fats and the objective is to minimize the cost to provide the diet.

In the 1980s, the University of New South Wales ran a program directed by Bruce Murtagh to offer companies student help with optimization problems at bargain consulting prices. I believe that $5000 was paid by a cat food company to determine an economical blend for tinned pet food. The resulting mixture, determined from a linear program, used ground up fish heads and fish oil with mostly grain components for a saving many times the consulting ...