Numerical Methods of Optimization MA 630 Darinka Dentcheva

Spring 2008 darinka.dentcheva@stevens.edu

Objective

The objective of this course is to introduce the students to the most popular numerical methods for solving nonlinear (non-smooth) optimization problems. The techniques will be based on the properties of nonlinear optimization models and the optimality conditions. Linear optimization techniques will be treated as a special case. Some examples using optimization software will be demonstrated in class.

Course Textbook

Andrzej Ruszczynski, Nonlinear Optimization, Princeton University Press, 2006,

ISBN: 0-691-11915-5

Time and Place

Lectures take place in Babbio center Room 319 on Thursdays 6:15 p.m. – 8:45 p.m.

Office hours: Peirce 302 on Tuesday 2:00 p.m. – 3:30 p.m. or by appointment.

Graded work:

The students will be assigned six projects involving the development, analysis and numerical solution of an optimization model.

Plan of lectures

Week	Date	Topic
1	Jan 17	Review of optimality conditions. Introduction to iterative methods.
2	Jan 24	Line search. Non-gradient methods.
3	Jan 31	Steepest decent method. Convergence analysis and conditioning.
4	Feb 7	Newton’s method. Conjugate gradient methods.
5	Feb 14	Conjugate direction without derivatives. Quasi-Newton methods.
6	Feb 21	Constrained Optimization: Projection.
7	Feb 28	The reduced gradient method. Penalty methods.
8	Mar 6	Dual methods.
9	Mar 13	Augmented Lagrangian methods.
10	Mar 27	Sequential quadratic programming methods. Barrier methods.
11	Apr 3	Nonsmooth optimization. Subgradient methods.
12	Apr 10	Cutting plane methods. Proximal point method.
13	Apr 17	Bundle methods.
14	Apr 24	Trust region methods. Non-convex constraints.