Optimization
| Code | School | Level | Credits | Semesters |
| MATH3051 | School of Mathematical Sciences | 3 | 20 | Autumn China |
- Code
- MATH3051
- School
- School of Mathematical Sciences
- Level
- 3
- Credits
- 20
- Semesters
- Autumn China
Summary
This is an introduction to fundamental aspects in mathematical optimization, with an emphasis on continuous and convex optimization and an outlook towards computational/applied mathematics and data science.
The module is structured around the following topics:
• Introduction to optimization: mathematical formulation and classification, examples, and convexity.
• Unconstrained optimization: gradient descent and line search methods, trust-region methods, linear and nonlinear least-squares problems.
• Constrained optimization: optimality conditions and Lagrange multipliers, linear programming and duality, penalties and the Augmented Lagrangian method.
• Stochastic optimization: stochastic gradient descent and nature-inspired optimization.
Target Students
Single Honours students from the School of Mathematical Sciences.Requisites:MATH1032 Probability, MATH1028 Analytical and Computational Foundations, MATH1027 Calculus, MATH1030 Linear Mathematics
Classes
- One 2-hour lecture each week for 12 weeks
- Two 1-hour lectures each week for 12 weeks
Two 1 hour lectures per week and one 2 hour lecture per week (one hour of which is a computer workshop).
Assessment
- 20% Coursework 1: Computing portfolio
- 20% Coursework 2: Computing Portfolio
- 60% Exam 1 (3-hour): Written examination
Assessed by end of autumn semester
Educational Aims
The purpose of this module is to introduce the students to the theory of mathematical optimization and its applications in science and engineering. The module aims at endowing the students with the necessary mathematical background and a consistent methodological toolbox, to formulate optimization problems and to effectively develop an algorithmic approach to its solution. The module is centred around classical optimization problems such as linear programming and nonlinear regression problems arising in a myriad of areas including operations research, computational data science, and financial mathematics, among many others.Learning Outcomes
A student who completes this module successfully should be able to:
L1 Formulate a mathematical optimization problem by identifying a suitable objective and constraints.
L2 Identify the mathematical structure of an optimization problem (linear/nonlinear, constrained/unconstrained, continuous/discrete, convex/non-convex) and to choose an algorithm approach consistent with this classification.
L3 Implement different computational optimization algorithms.
L4 To analyse the results of a computational optimization method in terms of optimality guarantees, sensitivities, and performance.