Numerical Methods for Nonlinear Programming Problems

The purpose of this paper is to describe some basic ideas of algorithms for solving nonlinear programming problems. A short description of optimality conditions in Section 3 is followed by a discussion of superlinearly convergent methods for unconstrained problems in Section 4. An extension of these methods for linearly constrained problems is outlined in Section 5. Nonlinear inequality constraints are discussed in Section 6. Problems of this type are usually solved by constructing and solving a sequence of simpler, i.e., unconstrained or linearly constrained, minimization problems. The final section deals with the application of automatic differentiation in nonlinear programming.