Optimization of a function f (x1, . . . ,xn) involves choosing the xi variables to make
the function f as large or as small as possible. With constrained optimization,
permissible choices for the xi are restricted or constrained. In what follows, such
constraints are represented by a function, g, whereby the xi variables must sat-
isfy a condition of the form g(x1, . . . ,xn) = c. For example, in the standard utility maximization problem, the task is to maximize utility u(x1, . . . ,xn) subject to a
budget constraint p1x1+·· ·+ pnxn = c, where pi is the price of good i and c is the income available.