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

COMPUTER USAGE:

  • 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.

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