CATALOG DESCRIPTION: Numerical solution of unconstrained optimization problems, nonlinear least squares and nonlinear systems of algebraic equations, large-scale nonlinear optimization, quadratic programming, and constrained optimization.
REQUIRED TEXTS: J. Nocedal and S. Wright, Numerical Optimization , Springer Verlag.
REFERENCE TEXTS: R. Fletcher, Practical Methods of Optimization , Wiley, 2nd edition
COURSE DIRECTOR: Jorge Nocedal
COURSE GOALS: Demonstrate the formulation, solution and analysis of optimization problems. Illustrate the difference between well-posed and ill-posed problems, and the analytical tools to examine the validity of the model and the meaning of the solution. Study modern algorithms for the solution of nonlinear optimization problems.
PREREQUISITES BY COURSES: IE 311, EECS 328
PREREQUISITES BY TOPIC:
- Basic knowledge of Calculus and Linear Algebra
- Programming experience
DETAILED COURSE TOPICS:
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
Week 7 Theory of Constrained Optimization
Week 8 Overview of Constrained Algorithms
Week 9 Sequential Quadratic Programming
Week 10 Augmented Lagrangian Methods
- Four or five computer projects will be given.
- Use of Matlab to facilitate analysis of data and the creation of graphics is encouraged.
LABORATORY PROJECTS: None.
GRADES: Homeworks – 100%
COURSE OBJECTIVES: When a student completes this course, s/he should be able to:
- Know how to model optimization problems and understand the distinction between linear, nonlinear and convex problems.
- Perform sensitivity analysis of models and suggest improvements in the model. Know the types of algorithms that are effective for each class of problems and understand their limitations.