Nonlinear Programming
A typical difficulty associated with nonlinear optimization
is the problem that in most cases it is only possible to determine a locally
optimal solution but not the global optimum. Loosely speaking, the global
optimum is the best of all possible values while a local optimum is the
best in a nearby neighborhood only.
Algorithms to Solve NLP Problems
Algorithms to solve NLP problems are found for instance
in Gill et al. (1981) or Fletcher (1987). Most of them are based
on linearization techniques. Inequality conditions are included for instance
by applying active sets methods. The most powerful nonlinear optimization
algorithms are the Generalized Reduced Gradient algorithm (GRG)
and sequential quadratic programming (SQP) methods. The GRG algorithm
was first developed by Abadie and Carpenter (1969) [more recent information
is contained in Abadie (1978), Lasdon et al. (1978) and Lasdon and
Waren (1978)]. For NLP problems with only a few nonlinear terms and in
particular NLP problems containing pooling problems recursion or
is frequently used.
