MA305 Half Unit

Optimisation in Function Spaces

**This information is for the 2019/20 session.**

**Teacher responsible**

Prof Adam Ostoja-Ostaszewski

**Availability**

This course is available on the BSc in Business Mathematics and Statistics, BSc in Mathematics and Economics, BSc in Mathematics with Economics, BSc in Mathematics, Statistics, and Business and BSc in Statistics with Finance. This course is available as an outside option to students on other programmes where regulations permit. This course is available with permission to General Course students.

**Pre-requisites**

Students should have attended a course in analysis, ideally **Real Analysis **(MA203)** **and a course** **in** **Mathematical Methods, ideally **Further Mathematical Methods** (MA212).

**Course content**

This is a course in optimisation theory using the methods of the Calculus of Variations. No specific knowledge of functional analysis will be assumed and the emphasis will be on examples. This course develops a geometric approach to those optimisation problems which involve the choice of functions. Applications relevant to Economic Theory are studied. It introduces key methods of continuous time optimisation in a deterministic context, including the Calculus of Variations, Pontryagin's Principle and Bellman's Principle. Specific topics include: Introductory examples. Calculus of variations. Euler-Lagrange Equations. Necessary conditions. Maximum Principle. Transversality conditions. Linear time-invariant state equations. Controlability. Dynamical programming. Applications to Economics.

**Teaching**

20 hours of lectures and 10 hours of classes in the LT. 2 hours of lectures in the ST.

**Formative coursework**

Written answers to set problems will be expected on a weekly basis.

**Indicative reading**

A full set of lecture notes will be provided, based on: A. Sasane, Optimization in function spaces, Dover, 2016; Useful reference text: D. G. Luenberger, Optimization by Vector Space Methods, Wiley, 1969.

**Assessment**

Exam (100%, duration: 2 hours) in the summer exam period.

**
Key facts
**

Department: Mathematics

Total students 2018/19: 3

Average class size 2018/19: 3

Capped 2018/19: No

Value: Half Unit

**Personal development skills**

- Self-management
- Problem solving
- Application of information skills
- Communication
- Application of numeracy skills
- Specialist skills