Complementarity theory - AbsoluteAstronomy.com

A complementarity problem is a type of mathematical optimization problem. It is the problem of optimizing (minimizing or maximizing) a function of two vector

Vector space

A vector space is a mathematical structure formed by a collection of vectors: objects that may be added together and multiplied by numbers, called scalars in this context. Scalars are often taken to be real numbers, but one may also consider vector spaces with scalar multiplication by complex...

variables subject to certain requirements (constraints) which include: that the inner product of the two variables must equal zero, i.e. <X, Y> = 0. In particular for finite-dimensional real vector spaces this means that, if one has vectors X and Y with nonnegative components (x_i ≥ 0 and y_i ≥ 0 for all

: in the first quadrant if 2-dimensional, in the first octant

Octant

An octant is one of eight divisions.-Octant in the plane :Traditionally wind direction is given as one of the 8 octants because that is more accurate than merely giving one of the 4 quadrants, and the wind vane typically does not have enough accuracy to bother with more precise indication.-Octant...

if 3-dimensional), then for each pair of components x_i and y_i one of the pair must be zero, hence the name complementarity.