Numerical Methods of Optimization MA 630 Darinka Dentcheva

Fall 2009 darinka.dentcheva@stevens.edu

Objective

The objective of this course is to introduce the students to the most popular numerical methods for solving nonlinear smooth and non-smooth optimization problems. The techniques will be based on the properties of nonlinear optimization models, the optimality conditions, and duality of convex optimization. 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 310 on Tuesdays 6:15 p.m. – 8:45 p.m.

Office hours: Peirce 302 on Monday 2:00 p.m. – 4:00 p.m. or by appointment.

Graded work:

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

Plan of lectures

Week	Date	Topic
1	Sep 1	Review of optimality conditions. Introduction to iterative methods.
2	Sep 8	Line search. Non-gradient methods.
3	Sep 15	Steepest decent method. Convergence analysis and conditioning.
4	Sep 22	Newton’s method. Conjugate gradient methods.
5	Sep 29	Conjugate direction without derivatives. Quasi-Newton methods.
6	Oct 6	Constrained Optimization: Projection.
7	Oct 20	The reduced gradient method. Penalty methods.
8	Oct 27	Dual methods.
9	Nov 3	Augmented Lagrangian methods.
10	Nov 10	Sequential quadratic programming methods. Barrier methods.
11	Nov 17	Nonsmooth optimization. Subgradient methods.
12	Nov 24	Cutting plane methods. Proximal point method.
13	Dec 1	Bundle methods.
14	Dec 8	Trust region methods. Non-convex constraints.