Kotlin and linear programming

> “Linear” means continuous

No. As in G. Simmons, the two pillars of the field of 'analysis' in math are linearity and continuity. The two are quite different.

Linearity usually has to do with numbers and vectors. The numbers are usually in the set R of real numbers or the set C of complex numbers. Commonly the numbers are called scalars. Then, a function f is 'linear' provided for scalars a and b and vectors x and y we have

f(ax + by) = af(x) + bf(y)

The role, utility? It's an enormous, powerful simplification and, in particular, is crucial to systems (high school style) 'systems of linear equations', linearity, essentially 'super position', in quantum mechanics, and linear operators, as in the classic Dunford and Schwarz, e.g., as in the results of S. Banach. In calculus, differentiation and integration are both linear operators.

And, in particular, linearity is crucial in both linear programming and integer linear programming. Local linear approximations are crucial in non-linear optimization, e.g., the Kuhn-Tucker conditions and their associated constraint qualifications.

Continuity is also a biggie, e.g., for a function to be continuous on a compact set, e.g., [0,1], means it is also uniformly continuous, bounded, and achieves its greatest lower bound and least upper bound. Continuity, compactness, and uniform continuity are the standard assumptions that guarantee that the Riemann integral of freshman calculus exists.

Maybe what was meant was usually when we mention linear programming we have, say, find x to solve Ax = b, x >= 0 where x, where for positive integer n, is n x 1 and, thus, for the set of real numbers R, in the set R^n. Here the A is a matrix, say, for some positive integer m, m x n. Then from the beginnings of the start of matrix theory, for real a and b and n x 1 y we have

A(ax + by) = aAx + bAy

which says that A is a linear function (operator, transformation, etc.). That's the 'linearity' in linear programming. And it holds in linear integer programming where we ask that some or all of the components of x be integers.

Adding to my other comment, my biggest dissatisfaction with this article is that all it did was show the quite excessively verbose problem setup, without actually showing an algorithm for integer linear programming. An interesting post would have explained how to implement branch and bound in Kotlin, not how to call somebody else's library. Needless to say, I'm not sold on Kotlin from reading this.

That there are dominant players in a field shouldn't preclude someone from trying. Especially if you see a face that could use help. Safety would be a good candidate here.

Python is often a second class citizen in these areas, even if much is made about its widespread support in the data science realm. I don't want to say it's hype is overblown... but a lot of the pain points and cracks in the seams are glossed over.

Take spark, for instance. You run into extreme performance issues the second your data has to be serialized to cross the py4j gap. An many essential parts of its API require scala/java (presumably Kotlin ought to work as well).

Similar situations occur all across the big data and cloud realm, with python. And then even still today.. you'll run into situations where whizzbang data science ml library that solves your exact problem.. for some reason is python 2.7 only. Thankfully that situation is getting rarer (there really isn't an excuse for it today) - but its still there.

In any case, a "not-java" language that can talk java is freakin amazing, in my book (Scala doesn't scratch my itch there - it's far too clever - had enough of that with perl back in the day).

If you want to integrate MIP / LP as one component of a larger production system, and you are already using kotlin / JVM ecosystem, then this could be an advantage.