Complementarity theory
Overview
 
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. <XY> = 0. In particular for finite-dimensional real vector spaces this means that, if one has vectors X and Y with nonnegative components (xi ≥ 0 and yi ≥ 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 xi and yi one of the pair must be zero, hence the name complementarity.
Quotations

This house is so full of people, it makes me sick! When I grow up and get married, I'm living alone!

[in his mind] I wish they would all just disappear.

I took a shower, washing every body part with actual soap, including all my major crevices, including in between my toes and in my belly button, which I never did before but sort of enjoyed. I washed my hair with adult-formula shampoo and used cream rinse for that just-washed shine. I can't seem to find my toothbrush, so I'll pick one up when I go out today. Other than that, I'm in good shape. [applies aftershave] AAAAAAAAAAAAAAAAAGHHHHHHHHHHHH!

A Family Comedy Without The Family.

When Kevin's Family Left For Vacation, They Forgot One Minor Detail: Kevin. But Don't Worry... He Cooks. He Cleans. He Kicks Some Butt.

This Non-Family Comedy is a Real Scream.

 
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