MATH66132/MATH46132: Numerical Optimisation

Lecturer:		Dr. C. Powell
Lectures:		Thursday 2pm-4pm, Friday 2pm-3pm.
Office Hour:		Thursday, 4pm-5pm
Location:		Alan Turing G.108
Problem Classes:		In even weeks ONLY, Thursday, 3pm-4pm slot.
Credits:		15

The materials provided on this page are for MSc students and 4th year undergraduates at the University of Manchester taking the courses MATH66132/MATH46132 only. Note that a shorter version of this course existed for many years at the University of Manchester and UMIST. In 2008, however, the course was been re-designed and extended.

Resources

Text books
Computing
Lecture Notes
Handouts
Problem sheets
Example codes
Coursework
Past exam papers

Text books

For the first part of the course (until Easter), the following references are the most relevant.

J. Nocedal and S.J. Wright. Numerical Optimization. Springer-Verlag, New York, 1999.
N. Gould and S. Leyffer. An introduction to algorithms for nonlinear optimization. In: frontiers in Numerical Analysis (Durham, 2002). Springer 2003.

Note that the first text is currently available online as an e-book from the UoM library webpage an can be downloaded free of charge by UoM students.

Computing

Students will be expected to use MATLAB throughout the course, both in coursework assignments and on a weekly basis to answer programming questions set on the problems sheets. The course is algorithmic in nature and many theoretical points are best illustrated via hands-on experience at a computer. MATLAB guides and manuals are readily available on the web and in the library. In addition, we will use MATLAB's optimization toolbox which is available on the School's linux cluster.

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Lecture Notes

Lectures will consist of computer presentations and demonstrations. Pdf files of the lectures (30 in total) will be posted here. Some material will be provided on handouts.

Lecture 1-2	Lecture 4	Lecture 7	Lecture 10	Lecture 13	Lecture 16	Lecture 19	Lecture 22	Lecture 25
	Lecture 5	Lecture 8	Lecture 11	Lecture 14	Lecture 17	Lecture 20	Lecture 23	Lecture 26
Lecture 3	Lecture 6	Lecture 9	Lecture 12	Lecture 15	Lecture 18	Lecture 21	Lecture 24

Handouts

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Problem Sheets

As a general rule one problem sheet covers two weeks worth of lectures. Students should attempt the questions and programming exercises prior to attending the examples classes. Solutions will be posted here later.

Sheet 1: and Solutions 1
Sheet 2: and Solutions 2
Sheet 3: and Solutions 3
Sheet 4: and Solutions 4 , KKT_data , my_minres.m , plot_p.m
Sheet 5: and Solutions 5
Sheet 6: and Solutions 6

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MATLAB Codes

Example MATLAB codes for the programming exercises will only be posted here after relevant assignments have been handed in.

quadratic_sd.m (Executes example from lecture 3 - steepest-descent with exact linesearch for quadratic objective function)
linesearch2 - inexact linesearch algorithm (SW conditions)
zoom - subroutine needed for linesearch2
GN_eg_data , gaussNewton - for question 5, examples sheet 3
bls (Armijo back-stracking linesearch)
inexact_sd (steepest descent with inexact line-search)
newton
nonlinear-cg
BFGS

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Coursework

The coursework component of this course comprises 25% of the total marks.

Coursework assignment 1 (Deadline: 27th March 2009) Solutions 1

Coursework assignment 2 - In-class test (Friday 8th May 2009)
I will distribute a set of questions in week 10 for you to prepare at home. I will pick one question for you to answer in exam conditions.

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Past exam papers

Since the course is partially new in 2008, there is only one past paper (see School of Maths website). Past papers for shorter versions of the course are also available. In 2009, the duration of the exam will be three hours and will consist of section A (compulsary) and section B (optional) questions.