Term  Explanation 
CobbDouglas function  f(x,y) = A x^{alpha} y^{beta},
example of an utility function.
x,y are usually referred as goods or bundles of goods 
Budget constraint  special constraint g(x,y) = c, the constant c is the
level of income 
Utility function  A function of two variables f(x,y) measuring
the level of utility, the variables x,y typically represent goods.
There can be more variables. 
Production function  A function of two variables f(x,y) measuring
the level of production, x,y typically are labor and capital.
There can be more variables. 
Cost function  A function of two variables f(x,y), where x,y are inputs
The function can be a constraint. There can be more variables. 
Objective function F  Function of several variables f, to be maximized or minimized. 
Program  Problem 
Duality  Maximizing utility given expenditures or minimizing expenditures by fixing utility.
Example in mathematics: minimize the surface area under
fixed volume or maximize the volume when surface area is fixed. 
Convex sets  A set Y is convex if for all a in [0,1], and all x,y in Y also
a x + (1a) y is in Y. Economists prefer convexity since in decision processes, one wants
to interpolate between two points x,y.

Convex function  A function is convex on a convex set S if
f(a*x + (1a) y) smaller or equal than a*f(x) + (1a)*f(y) for all a in [0,1] and all x,y in S.
Example: f(x,y) = x^{2}+y^{2} is convex.
A function is concave on S, if f is convex on S.

Quasiconvex function  An utility function f(x,y) is quasiconvex if the lower level sets Y_{c} = { f(x,y) smaller or equal than c }
are convex sets. Example: f(x,y) = xy is quasiconvex on the first quadrant S. Note that it is not convex
because 1 = f( (1,1)) = f( 1/2( (0,0) + (2,2) ) ) is smaller than 1/2 [ f( (0,0)) + f (2,2)) ] = 2.

Quasiconcave function  Utility function f(x,y) is quasiconcave if f is quasiconcave. Equivalently, the upper level sets
Y_{c} = { f(x,y) larger or equal than c } are convex sets. CobbDouglas functions like f(x,y) = 3 x^{2} y^{3}
are quasiconcave. (*)

Programming problem:  Find the global minimum f on the region G defined by
h_{i}=0, g_{j} less or equal to 0 
Linear programming problem:  Programming problem, where f and g_{i},h_{j} are all linear. 
Convex programming:  The function f and the contraints g_{j} are all convex 
Quadratic programming:  Contraints are linear, the objective function is a sum of
a linear function and a quadratic form. 
KuhnTucker conditions  Conditions for global minimum: convex f,g_{i}, affine h_{j} 