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*.