Non-linear Optimization (U01879)

? Credit Points : 10 ? SCQF Level : 11 ? Acronym : MAT-4-NLO

Unconstrained optimization: steepest descent and the line search problem. Method of conjugate gradients for minimization of a quadratic function. Newton's method, Newton-Raphson for solving a well-determined system of nonlinear equations. Linear and nonlinear least squares problems, Gauss-Newton method.

Constrained optimization: first and second order necessary and sufficient conditions for a local minimizer of a function subject to linear equality and inequality constraints.

Interval methods: Basic rules. Conditions affecting the quality of bounds. Interval form of Taylor's expansion.
Global optimization: Branch and bound using function bounds only. Using bounds on first and second derivatives. Interval Newton method.

Equation solving: Generating interval linear equations in Newton's method. Solving interval linear equations by interval Gaussian elimination and interval Gauss Seidel.

Entry Requirements

? Pre-requisites : Passes at C or better in MAT-2-FoC, MAT-2-SVC, MAT-2-LiA, MAT-2-MAM

Variants

? This course has variants for part year visiting students, as follows

Non-linear Optimization (VS1) (Semester 1 (Blocks 1-2))

Subject Areas

Home subject area

Specialist Mathematics & Statistics (Honours), (School of Mathematics, Schedule P)

Delivery Information

? Normal year taken : 4th year

? Delivery Period : Semester 1 (Blocks 1-2)

? Contact Teaching Time : 2 hour(s) per week for 11 weeks

First Class Information

Date	Start	End	Room	Area	Additional Information
20/09/2007	12:10	13:00	Lecture Room 6206, JCMB	KB

All of the following classes

Type	Day	Start	End	Area
Lecture	Monday	12:10	13:00	KB
Lecture	Thursday	12:10	13:00	KB

Summary of Intended Learning Outcomes

1. Applying the method of conjugate gradients to a quadratic optimization problem
2. Applying steepest descent or Newton's method, together with a line search, to a multidimensional unconstrained optimization problem.
3. Deriving the Newton-Raphson iteration scheme for a given nonlinear system.
4. Applying the Gauss-Newton method to a nonlinear least squares problem
5. Applying the first and second order necessary and sufficient conditions for a local minimizer to a specific example or class of problem.
6. Performing calculations using interval methods.
7. Recognising how to rearrange functions and use Taylor expansions to obtain tight bounds on function values.
8. Using branch and bound and Newton's method to find the global minima of functions of one and more variables.
9. Solving systems of interval linear equations and using this to guarantee finding all solutions of nonlinear equations.