Unit name | Optimisation 2 |
---|---|
Unit code | MATH20600 |
Credit points | 20 |
Level of study | I/5 |
Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |
Unit director | Dr. Misha Rudnev |
Open unit status | Not open |
Pre-requisites |
MATH11002 and MATH11003 |
Co-requisites |
None |
School/department | School of Mathematics |
Faculty | Faculty of Science |
Methods for finding (local or global) maxima or minima of functions of 1 or more variables, particularly when subject to constraint. Linear programming and non- linear minimisation, including results where convexity is relevant, such as the Kuhn-Tucker theorems. Applications in industry and economics. The emphasis is on practical techniques for solution of specific problems, but enough theory is given to provide a solid foundation for them. Some numerical work is included.
Aims:
To introduce students to mathematical foundations of linear and nonlinear optimisation.
Syllabus
The number of lectures shown is approximate. Some miscellaneous items may be added/removed throughout the course.
Introduction (2). Linear programming: the Simplex Method (7), sensitivity, duality, convexity and Farkas alternative (8). Applications in Game theory (2, if time allows).
Non-linear problems: unconstrained maxima and minima for functions of n variables, the Hessian and convexity, Jensen's inequality and corollares (5); problems with equality constraints; Lagrange multipliers (3); problems with inequality constraints; the Kuhn-Tucker conditions (6).
Note: There are 33 hours listed here. The remaining hours (out 36 available) will be devoted to additional topics, worked examples, discussions of difficult points, etc.
Approximately one week before the exam, a review session will be held.
Relation to Other Units
Related material is in the Engineering Mathematics unit Optimisation Theory and Applications. Students may not take both units.
At the end of the unit students should be able to:
Transferable Skills:
This is an eclectic course with relevance to a wide spectrum of Maths. Intelligence and imagination; mathematical formulation of complex "real-world" problems that are presented in continuous prose; communication to non-mathematicians of the results of a mathematical investigation.
Lectures; discussions in Problems classes. Homework will be of critical importance and an average student is expected to invest some 5 hours a week into it. There is a lot of software, designed for optimisation, some being available online, yet using it is not part of the course. Students are expected to do independent study and reading.
The final assessment mark for the unit is calculated 100% from a standard rubric examination in April. This means a 2½-hour written exam consisting of FIVE questions; your best FOUR will be counted towards the exam mark. Candidates may bring one A4 double-sided sheet of notes into the exam. Calculators of an approved type (non-programmable, no text facility) are permitted in the examination.
There will be no regular printed notes distributed, yet the course is accompanied by a series of handouts which address the majority of the difficult issues involved.
The unit is not based on a single book, and there is no mandatory text. However, the following books are highly recommended. There are many other texts covering various parts of the unit: try browsing in the shelves QA402 and T57 in Queen's Building Library. They can be used to get different perspectives on the material covered.