Course Outline

Instructor: Manfred Trummer Office: SSC 10517

Text: PERESSINI, SULLIVAN, AND UHL, The Mathematics of Nonlinear Programming. Springer Verlag.

Optimization is a key factor in the solution of a variety of problems in science, engineering, and business. This course will provide you with the mathematical foundations of optimization. A strong emphasis is on the constructive, algorithmic approach. Some optimization methods will be implemented numerically.

• Unconstrained Optimization.
  1. Review of linear algebra results.
  2. Necessary and sufficient conditions for a minimum.
  3. Functions of several variables.
  4. Newton's method.
  5. Steepest Descent. Quasi-Newton methods.
  6. Conjugate gradient methods.

• Constrained Optimization.
  1. Surfaces and Tangent planes.
  2. Lagrange multipliers.
  3. Kuhn-Tucker conditions.

There is NO final exam for this course.