What will you learn on this course?
Optimisation deals with the problem of minimising or maximising a
mathematical
model of an objective function such as cost, energy,
approximation error
and so forth under a set of side constraints on the domain of
definition of
this function. Optimisation theory deals with the mathematical
properties
of optimisation problems and the analysis of algorithms for their
solution.
The aim of this course is to provide an introduction to nonlinear
continuous
optimisation specifically tailored to the background of mathematics
students.
Who is teaching?
- Lecturer: Raphael Hauser. Comlab office 213, email hauser at
comlab
dot ac dot uk.
- Class Tutor: Coralia Cartis. Comlab office 207, email ccartis at
comlab
dot ac dot uk.
- Marker: Nicolas Jannequin. Email nicj at comlab dot ac dot uk.
How is this course organised?
The course consists of lectures and classes, but no practicals.
Students
hand in solutions to seven problem sheets which will be discussed in
classes
during weeks 2-8 of the term. Lectures are taking place in weeks 1-8 of
HT05
on Tuesdays and in weeks 2-8 on Fridays 2-3pm in Room 147 of the Comlab. On Friday
2-3pm
of week 1 the lecture takes place in Comlab 051. Classes take place in
Comlab
243, Tuesdays 4-5pm, weeks 2-8. Solutions have to be handed in by noon
on
Mondays before class. Mark them "for N. Jeannequin" and hand them in at
the
Comlab reception. See also the course outline slides and
the
syllabus.
Course materials
Each lecture is accompanied by a lecture note that explains the
material
in further detail. These notes will be posted here and form a
self-contained
introduction to the subject. They constitute compulsory reading
assignments.
Suggestions on how to improve the lecture notes are always very
welcome! Further
reading is also recommended from the book of Jorge Nocedal and Steve
Wright
"Numerical Optimization", Springer 1999. In addition, I will post transparencies of the actual lectures, problem
sheets
and sample exams for the revision classes in TT05. All materials are
posted
in PDF format. In order to display it, you need the Acrobat software,
which
is installed on almost all PCs and workstations. If you are
experiencing
problems downloading some of the materials, please contact me via email.
Chapter I: Unconstrained Optimisation.
- Lecture 1: introduction and preliminaries. Notes,
slides.
- Lecture 2: the descent method and line searches. Notes, slides.
- Lecture 3: steepest descent and Newton methods. Notes, slides.
- Lecture 4: quasi-Newton methods. Notes,
slides.
- Lecture 5: conjugate gradients and the Fletcher-Reeves method. Notes, slides.
- Lecture 6: trust region methods. Notes,
slides.
- Lecture 7: the dogleg and Steihaug methods. Notes, slides
Chapter II: Constrained Optimisation
- Lecture 8: the fundamental theorem of linear inequalities. Notes, slides.
- Lecture 9: first order necessary optimality conditions (KKT). Notes, slides.
- Lecture 10: second order optimality conditions. Notes, slides.
- Lecture 11: the method of Lagrange multipliers, examples. Notes.
- Lecture 12: Lagrangian Duality and Convex Programming. Notes, slides.
- Lecture 13: the penalty function method. Notes,
slides.
- Lecture 14: the augmented Lagrangian method. Notes, slides.
- Lecture 15: the barrier method for nonlinear programming. Notes, slides.
- Lecture 16: primal-dual path-following for linear programming. Notes, slides.
Problem sheets
Revision material
Revision classes
- I would like to hold two revision classes to discuss the sample exams 1
and 2. For this purpose I reserved Room 051 (Comlab) from 4-5pm on Thursdays
of weeks 2
and 3 of TT05. Please let me know as soon as possible if you have a conflict
with these times. If you would like to get your work marked (this
is optional), please hand it in at the Comlab Reception by Tuesday evening
marked "for Raphael Hauser".
Related websites
There are a wealth of web sites with information regarding to
optimisation:
learning materials, software, online tutorials, job opportunities,
internships
in companies, studentships and graduate programmes in operations
research,
professional associations ...
For a start, try the following links, or use a search engine: