ABSTRACT
In this chapter we consider the problem of optimizing a non-linear function subject to a finite collection of non-linear constraints. This is called non-linear programming (NLP). Let M = {1, 2, . . . ,m} be an index set. For each i ∈ M we have a continuous and differentiable function f i : Rn → R that will give rise to a constraint. The objective function will be f 0: Rn → R and is assumed to be continuous and differentiable. The problem (P) we consider is
max{f 0(x): f i(x) ≥ 0, ∀i ∈ M}. (P)
Any NLP can be transformed into the above form, however unlike the LP case, there are pitfalls for the careless.
