Module manager: Professor C.A. Jones
Email: pmtcaj@leeds.ac.uk
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2011/12
MATH1331 and MATH1050, or equivalent.
This module is not approved as an Elective
Optimisation ''the quest for the best'' plays a major role in financial and economic theory, eg in maximising a company's profits or minimising its production costs. How to achieve such optimality is the concern of this course, which develops the theory and practice of maximising or minimising a function of many variables, either with or without constraints. This course lays a solid foundation for progression onto more advanced topics, such as dynamic optimisation, which are central to the understanding of realistic economic and financial scenarios.
To provide a collection of theoretical and algorithmic techniques for determining optimal extrema of arbitrary functions of several variables, either with or without constraints.
On completion of this module, students should be to:
(a) determine the definiteness of quadratic forms;
(b) determine exactly extrema of functions of several variables, with or without constraints, using Lagrange multipliers;
(c) use the calculus of variations to determine extrema of integrals dependent upon one or more arbitrary functions;
(d) determine approximately extrema of functions of several variables, with or without constraints, using a selection of search algorithms.
Several-variable calculus, (6 lectures):
- Representing and visualising functions of 2 variables
- Partial derivatives, total derivatives and chain rule
- Gradient vectors and directional derivatives
- Implicit differentiation, change of variables, Jacobian
- Several-variable Taylor series
- Hessian matrix, stationary points.
Unconstrained optimisation (4 lectures):
- Quadratic forms and eigenvalues
- Definiteness using principal minor tests
- Stationary points, local extrema, unconstrained optimisation, applications in economics
- Cobb-Douglas production functions.
Constrained optimisation (10 lectures):
- Constrained maximisation with equality constraints
- Jacobian derivative
- first-order conditions
- constraint qualifications
- Lagrange multipliers
- constrained quadratic forms
- bordered Hessian
- constrained maximisation with inequality constraints and mixed constraints
- constrained minimisation
- Kuhn-Tucker theory (with applications in economics), economic interpretation of Lagrange multipliers, second-order conditions, bordered Hessian of Lagrangian.
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Workshop | 10 | 1 | 10 |
| Lecture | 22 | 1 | 22 |
| Private study hours | 68 | ||
| Total Contact hours | 32 | ||
| Total hours (100hr per 10 credits) | 100 | ||
Regular problem solving assignments
| Assessment type | Notes | % of formal assessment |
|---|---|---|
| In-course Assessment | four assessed example sheets | 15 |
| Total percentage (Assessment Coursework) | 15 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
| Exam type | Exam duration | % of formal assessment |
|---|---|---|
| Standard exam (closed essays, MCQs etc) | 2.0 Hrs Mins | 85 |
| Total percentage (Assessment Exams) | 85 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
The reading list is available from the Library website
Last updated: 2/27/2012
Errors, omissions, failed links etc should be notified to the Catalogue Team