a repository of mathematical know-how

Techniques for maximizing and minimizing

Quick description

Many important problems in mathematics concern the maximizing or minimizing of some quantity. This article contains links to articles about techniques for doing this.

Extremal combinatorics front page

Extremal combinatorics is the branch of combinatorics devoted to finding combinatorial structures, such as graphs or subsets of the discrete cube, that maximize or minimize certain quantities subject to certain constraints.

A typical example of a variational problem is to calculate the shape that a chain will form if its two ends are fixed. This is equivalent to minimizing the energy of the chain subject to certain constraints. The technique used to solve this problem is to find a local minimum by considering small variations to the position of the chain. However, this is more complicated than an elementary calculus problem because the space of possible positions of the chain is infinite dimensional.

Note iconIncomplete This article is incomplete. This article is far from complete.


Post new comment

(Note: commenting is not possible on this snapshot.)

Before posting from this form, please consider whether it would be more appropriate to make an inline comment using the Turn commenting on link near the bottom of the window. (Simply click the link, move the cursor over the article, and click on the piece of text on which you want to comment.)