The goal of an optimization problem can be formulated as follows: find the combination of parameters (independent variables) which optimize a given quantity, possibly subject to some restrictions on the allowed parameter ranges. The quantity to be optimized (maximized or minimized) is termed the objective function; the parameters which may be changed in the quest for the optimum are called control or decision variables; the restrictions on allowed parameter values are known as constraints.
A maximum of a function 
is a minimum of 
. Thus, the general
optimization problem may be stated mathematically as:
where 
is the objective function, 
is
the column vector of the 
independent variables, and
is the set of
constraint functions. Constraint equations of the form
are termed
equality constraints, and those of the form
are inequality
constraints. Taken together, and
are known as the problem functions.
