What does "programming" mean in mathematics?

Question

In the past few years, I have came across some topics in Math and CS that have the word "programming" in them. For example, there are linear programming, quadratic programming and dynamic programming. However, I find it hard to pin down what "programming" mean.

A standard dictionary defines "programming" either as the act of instructing a computer to do certain things based on computer code or as the act of organizing and arranging things. But the way "programming" is used in the aforementioned topics seem to be more related to the act of optimization.

More generally it means casting a problem in a form that allows us to find a solution. For example, dynamic programming is a technique for embedding a specific problem in a larger family of problems in a way that makes it easier to solve. — hardmath, Jul 03 '20 at 15:55

Théophile · Accepted Answer · 2020-07-03T16:05:03.697

These optimization problems are called "programs" for historical reasons. The methods were developed in the 1940s, some time before there was a more standard usage of the term "programming".

Here are several resources. The first two are very quick to read; the third goes into a more detailed history:

an answer on mathoverflow.net that gives some more context;
a similar question on math.stackexchange with an insightful answer; and
a paper titled A Brief History of Linear and Mixed-Integer Programming Computation.

score 0 · Answer 2 · answered Jul 03 '20 at 15:43

Linear programming is the study of optimizing "linear programs". Here is an example:

max $x_1 + x_2$

subject to

$3x_1 -x_2 \leq 5$

$x_2 \leq 3$

$x_1, x_2 \geq 0$

We optimize a linear function according to some constraints. Programming and optimization are sometimes words that are used interchangably.

What does "programming" mean in mathematics?

2 Answers2

Linked