Title

Nonlinear Programming
Author

 Daniel Lichtblau
 Organization: Wolfram Research, Inc.
Education level

College
Objectives

We cover "classical" local root-finding and optimization techniques for differentiable functions (in some cases classical means 17th century, in others it might be circa 1970!). We also cover some geometric programming. The objectives are to introduce students both to the relevant mathematical theory and to the algorithmic side of the field (some of that latter emphasis was added by myself). I developed the Mathematica courseware as a complement to the standard textbook material. My own objective was to introduce students to the beauty of programming the methods only sketched in the text, to indicate what must be done to make algorithms that are practical, discuss some tradeoffs between various methods, and so on.
Materials

The Mathematics of Nonlinear Programming by Peressini, Sullivan, Uhl, (Springer-Verlag Undergraduate Texts in Mathematics, 1988)
Description

This is an introductory graduate-student course in nonlinear programming. The focus is on theory and algorithmic methods for solving equations and for the related task of local optimization. Upper undergrad/beginning grad level (more the latter than the former).

The courseware shows how one can attack nontrivial problems using Mathematica. It also goes into details about methods, subtleties, and so on that are not covered in the book.

Several students found the code provided in the notebooks to be quite helpful for homework problems. Some of the more advanced students found the examples and finer points to their liking.

Topics:
• Optimization by methods of multivariate calculus and linear algebra
• Unconstrained geometric programming via convex functions
• Iterative methods Newton's, steepest-descent, quasi-Newton methods) for root-finding and optimization
• Linear least-squares methods
• Constrained programming via multipliers
• Penalty methods
Subject

 Applied Mathematics > Optimization