Nonlinear Programming: Introduction, Unconstrained Nonlinear Programming, Constrained Nonlinear Programming

Nonlinear Programming (NLP) is the broad area of applied mathematics that addresses optimization problems when nonlinearity in the functions are envolved. In this chapter we introduce the problem, and making reference to the smooth case, we review the standard optimality conditions that are at the basis of most algorithms for its solution. Then, we give basic notions concerning the performance of algorithms, in terms of convergence, rate of convergence, and numerical behaviour.