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.

Operations Research Models and Methods
by Paul A. Jensen & Jonathan F. Bard
Copyright 2001 - All rights reserved