problems in all areas of mathematics, applied science, engineering, economics, medicine and statistics can be posed as mathematical optimization problems. an optimization problem begins with a set of independent variables, and often includes conditions or restrictions that define acceptable values of the variables. such restrictions are known as the constraints of the problem. the other essential component of an optimization problem is a single measure of "goodness", termed the objective function, which depends in some way on the variables. the solution of an optimization problem is a set of allowed values of the variables for which the objective function assumes its "optimal" value. in mathematical terms, this usually involves maximizing or minimizing.