Goals:
The course focuses on the formulation, solution and analysis of nonlinear optimization problems. It illustrates the difference
between well-posed and ill-posed problems, and how the solutions are characterized.  Modern techniques for solving nonlinear optimization problems are discussed in detail

The text book is Numerical Optimizationi, 2nd Edition, by J. Nocedal and S. Wright, Springer Verlag, 2006. Most of the topics covered in the course will be based on this book. There will be weekly assignments.  Most assignments consist of pencil-and-paper problems and short computer program. Knowledge  of computer programming (with any language such as C, C++ or Matlab) is required.

Prerequisites: Multivariable calculus, linear algebra and computer programming. No prior knowledge of optimization is assumed.
 

Course Outline

•   week 1:         Modeling Practical Problems
•   week 2:         Fundamentals of Unconstrained Minimization
•   week 3:         Line Search Methods
•   week 4:        Trust Region Methods
•   week 5:        Practical Newton Methods
•   week 6:        Differentiation
•   weeks7-8:    Theory of Constrained Optimization
•   week 9:        Overview of Constrained Algorithms
•   week 10:     Sequential Quadratic Programming