Math 287 - Nonlinear Optimization

    Math 287 is an introduction to the theory and practice of nonlinear
optimization.  Optimization occurs whenever you wish to find the best way to
do something, and all areas of science and engineering, and even many areas
in the humanities, make use of it.  Nonlinear optimization deals with the
most general continuous optimization problems, which occur very frequently,
for example, in engineering applications.

    The course begins with an introduction to how real world problems can be
modelled as mathematical optimization problems.  We discuss the basic theory
of unconstrained optimization, including the important idea of convexity.  We
look at methods for 1-dimensional unconstrained optimization, such as
Newton's method, the bisection method, the Golden Section method, and
interpolation methods.  We then look at methods for n-dimensional
unconstrained optimization, including methods that use second derivatives
(Newton's), first derivatives (steepest descent, quasi-Newton, conjugate
gradient) and no derivatives.  Approaches such as line search and trust
regions are discussed.  We investigate the
basic theory of constrained optimization, particularly the Karush-Kuhn-Tucker
conditions.  Then we examine methods for constrained optimization, including
Sequential Quadratic Programming and barrier/penalty function methods.

    Note that you do NOT need to have taken Math 288/CS 257, Linear
Optimization, in order to take Math 287.  Prerequisites are multivariable
calculus, linear algebra, and a computer programming course.

    The course is suitable for graduate students and upper-level
undergraduates.