Math 288/CS 257 - Linear Optimization

    Math 288 is an introduction to the theory and practice of linear
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.  Linear optimization is a special
well-solved case of the general optimization problem, and has applications to
many disciplines.

    The first half of the course concentrates on the basic theory of linear
programming, developed in conjunction with a discussion of the classic
algorithm for solving linear programs, known as the Simplex Method.  We look
at linear program models for real problems, feasibility and boundedness, the
Simplex Method (both the basic method and the two-phase method), duality,
complementary slackness, the Dual Simplex Method, and sensitivity analysis.

    The second half of the course investigates several further aspects of
linear programming.  First, we look at newer methods for linear programming,
the Ellipsoid Method and Interior Point Methods.  Then we will look at
applications of linear programming to solving problems of combinatorial
optimization, such as network problems like shortest path or maximum flow. 
In particular we cover as many as we can of integer programming and total
unimodularity, cutting planes, branch-and-bound, and the primal-dual
algorithm.

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

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