ABSTRACT
Mathematical programming is the finite dimensional branch of optimization theory in which a single-valued objective function f on n real variables x1 ..., xn is minimized (or maximized), possibly subject to a finite number of constraints, which are written as inequalities or equations. Generally we define a mathematical program of, say, minimization as
(MP) min f(x) (1)
subject togi(x) ≥ 0, i = 1, ..., m (2)
hj(x) =0, j = 1, ..., p (3)
where x denotes the column vector whose components are x1, ..., xn. In other words, (MP) is the problem of finding a vector x* that satisfies (2) and (3) and such that f(x*) has a minimal—that is, optimal value. If one or more of the functions appearing in (MP) are nonlinear in x, we call it a nonlinear program, in contrast to a linear program, where all these functions must be linear.