Undergraduate Course: Non-linear Optimization (MATH11045)
Course Outline
| School |
School of Mathematics |
College |
College of Science and Engineering |
| Course type |
Standard |
Availability |
Available to all students |
| Credit level (Normal year taken) |
SCQF Level 11 (Year 4 Undergraduate) |
Credits |
10 |
| Home subject area |
Mathematics |
Other subject area |
Specialist Mathematics & Statistics (Honours) |
| Course website |
http://student.maths.ed.ac.uk |
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|
| Course description |
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.
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Course Delivery Information
|
| Delivery period: 2010/11 Semester 1, Available to all students (SV1)
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WebCT enabled: Yes |
Quota: None |
| Location |
Activity |
Description |
Weeks |
Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
| King's Buildings | Lecture | | 1-11 | | | | 12:10 - 13:00 | | | King's Buildings | Lecture | | 1-11 | 12:10 - 13:00 | | | | |
| First Class |
First class information not currently available |
|
| Delivery period: 2010/11 Semester 1, Part-year visiting students only (VV1)
|
WebCT enabled: Yes |
Quota: None |
| Location |
Activity |
Description |
Weeks |
Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
| King's Buildings | Lecture | | 1-11 | | | | 12:10 - 13:00 | | | King's Buildings | Lecture | | 1-11 | 12:10 - 13:00 | | | | |
| First Class |
Week 1, Wednesday, 11:10 - 12:00, Zone: King's Buildings. JCMB, room 1501 |
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. |
Assessment Information
Examination only.
Visiting Student Variant Assessment
Examination only. |
| Please see Visiting Student Prospectus website for Visiting Student Assessment information |
Special Arrangements
| Not entered |
Contacts
| Course organiser |
Dr Liam O'Carroll
Tel: (0131 6)50 5070
Email: L.O'Carroll@ed.ac.uk |
Course secretary |
Mrs Alison Fairgrieve
Tel: (0131 6)50 6427
Email: Alison.Fairgrieve@ed.ac.uk |
|
copyright 2010 The University of Edinburgh -
1 September 2010 6:19 am
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