

Nonlinear
Programming Supplements


Supplements
are PDF files covering subjects not included in the textbook.



Separable programming is important because it allows a convex
nonlinear program to be approximated with arbitrary accuracy with
a linear programming model. The idea is to replace each nonlinear
function with a piecewise linear approximation. Global solutions
can then be obtained with any number efficient LP codes. 


A linearly constrained optimization problem with a quadratic objective
function is called a quadratic program (QP). Because of its many
applications, quadratic programming is often viewed as a discipline
in and of itself. More importantly, though, it forms the basis
of several general nonlinear programming algorithms. 


In solving a nonlinear program, primal methods work on the original
problem directly by searching the feasible region for an optimal
solution. Each point generated in the process is feasible and
the value of the objective function constantly decreases. These
methods have three significant advantages: (1) if they terminate
before confirming optimality (which is very often the case with
all procedures), the current point is feasible; (2) if they generate
a convergent sequence, it can usually be shown that the limit
point of that sequence must be at least a local minimum; (3) they
do not rely on special structure, such as convexity, so they are
quite general. 
