EEC254 – Optimization
3 units – Winter Quarter; alternate years
Lecture: 3 hours
Prerequisite: Math 22A; knowledge of FORTRAN or C
Grading: Letter; homework (60%) and final examination (40%).
Modeling optimization problems existing in engineering design and other applications; optimality conditions; unconstrained optimization (gradient, Newton, conjugate gradient and quasi-Newton methods); duality and Lagrangian relaxation; constrained optimization (Primal method and an introduction to penalty and augmented Lagrangian methods).
Expanded Course Description:
- Modeling Optimization Problems
- Evolution of optimization-based engineering design
- Modeling optimization problems existing in a variety of engineering design situations
- Unconstrained Optimization
- First- and second-order optimality conditions
- Convergence and rate of convergence
- Univariate Optimization
- Various methods (including Fibonacci search, golden section, and curve fitting) for one-dimensional minimization
- Basic Descent Methods
- Steepest descent and Armijo gradient algorithms
- Newton’s method and local convergence
- Conjugate Gradient Method
- Conjugate directions
- Conjugate gradient algorithm
- Rate of convergence
- Partial conjugate gradient method
- Quasi-Newton Methods
- Variable metric concept
- Rank one and rank two updates of the approximate Hessian
- Constrained Minimization
- Optimality conditions
- Local duality and Lagrangian relaxation
- Primal Methods
- Active set method
- Gradient projection method
- Other Methods
- Penalty and barrier methods
- Augmented Lagrangian methods
- Linear and Nonlinear Programming, Second Edition, David G. Luenberger, Addison-Wesley, 1984.
- Nonlinear Programming, Dimitri P. Bertsekas, Athena Scientific, 1995.
THIS COURSE DOES NOT DUPLICATE ANY EXISTING COURSE.
Last revised: February 1997