2015/16 Undergraduate Module Catalogue
MATH2640 Introduction to Optimisation
10 creditsClass Size: 180
Module manager: Professor F Nijhoff
Email: F.W.Nijhoff@leeds.ac.uk
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2015/16
Pre-requisite qualifications
MATH1010 or (MATH1050 and MATH1060) or (MATH1050 and MATH1331), or equivalent.This module is approved as a discovery module
Module summary
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.Objectives
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) determine extrema of functions of several variables subject to inequality constraints, using both classical and Kuhn-Tucker approaches;
(d) apply the theory to a range of problems arising in Mathematical Economics.
Syllabus
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
- Application to mean-variance portfolio theory and the Markowitz model
Teaching methods
Delivery type | Number | Length hours | Student hours |
Workshop | 10 | 1.00 | 10.00 |
Lecture | 22 | 1.00 | 22.00 |
Private study hours | 68.00 | ||
Total Contact hours | 32.00 | ||
Total hours (100hr per 10 credits) | 100.00 |
Private study
Studying and revising of course material.Completing of assignments and assessments.
Opportunities for Formative Feedback
Regular problem solving assignmentsMethods of assessment
Coursework
Assessment type | Notes | % of formal assessment |
In-course Assessment | four assessed example sheets | 15.00 |
Total percentage (Assessment Coursework) | 15.00 |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
Exams
Exam type | Exam duration | % of formal assessment |
Standard exam (closed essays, MCQs etc) | 2 hr | 85.00 |
Total percentage (Assessment Exams) | 85.00 |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
Reading list
The reading list is available from the Library websiteLast updated: 16/04/2015
Browse Other Catalogues
- Undergraduate module catalogue
- Taught Postgraduate module catalogue
- Undergraduate programme catalogue
- Taught Postgraduate programme catalogue
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