Optimization is of fundamental importance in virtually all branches of science and technology. As a consequence, optimization methods find their applications in numerous fields, starting from, e.g., network flow and ranging over shape optimization in engineering to optimal control problems. This course provides an introduction into the most important methods and techniques in discrete and continuous optimization. We will present, analyze, implement, and test methods for discrete and continuous optimization. This will include optimality conditions, the handling of linear and non-linear constraints, and methods such as interior point methods for convex optimization, Newton's method, Trust-Region methods, and optimal control methods. Furthermore, we will consider fast and massively parallel iterative solution methods such as multigrid and domain decomposition, which are needed for solving the arising large scale linear sub-problems. By combining both method classes, we will eventually derive efficient optimization and solution methods for large scale optimization and minimization problems.
Numerical Optimisation; Nocedal, Jorge, Wright, Stephen; Series: Springer Series in Operations Research and Financial Engineering, 2nd ed., 2006, XXII, 664 p. 85 illus., www.springer.com/mathematics/book/978-0-387-30303-1
A Multigrid Tutorial; William L. Briggs, Van Emden Henson, and Steve F. McCormick; Second Edition, SIAM, 2000 (book home page), ISBN 0-89871-4621.
Multigrid Methods and Applications; Wolfgang Hackbusch; Springer, 1985.
An Introduction to Multigrid Methods; Pieter Wesseling; Corrected Reprint. Philadelphia: R.T. Edwards, Inc., 2004. ISBN 1-930217-08-0.
Matrix computations; Gene H. Golub and Charles F. Van Loan.
Domain Decomposition Methods; Toselli, Widlund
Trust-Region Methods; Conn Gould Toint.
Practical Methods of Optimisation; R. Fletcher.