CMSC 34500
OptimizationPrerequisites: Some knowledge of linear Algebra, advanced calculus and a program language (can be Fortran, C, C++ or Matlab etc).
Catalog Description: Optimization is an important tool in an enormous range of applications in the sciences, engineering, and finance. In mathematical terms, optimization algorithms seek to find the minimum or maximum of a function of several (possibly many) variables, where the variables often must satisfy certain constraints.
In this course, we describe algorithms for solving several types of optimization problems, discussing their mathematical properties, their software implementations, and key applications. The particular choice of topics will depend on the interest of students in the class.
Long Description: Intended Synopsis for Autumn 2008: Roughly, the following materials will be covered in class:
1. Introductory remarks about numerical optimization
2. Theory for unconstrained optimization (including optimality conditions and more)
3. Line-search methods for unconstrained optimization
4. Linear and nonlinear conjugate gradient methods
5. Newton and quasi-Newton methods for unconstrained problems
6. Trust-region methods for unconstrained minimization
7. General theory of constrained optimization
8. The simplex method and the interior point method for linear programming with constraints
9. Introduction to sequential quadratic programming for constrained optimization
Textbook: J. Nocedal and S. Wright, Numerical Optimization, Springer Verlag, 1999
Instructors: Kui RenQuarter offered: Autumn 2008
Last Verified by Stephen Wright on 19 February, 2001.