Optimization
| Code | School | Level | Credits | Semesters |
| MATH3027 | Mathematical Sciences | 3 | 20 | Autumn UK |
- Code
- MATH3027
- School
- Mathematical Sciences
- Level
- 3
- Credits
- 20
- Semesters
- Autumn UK
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. (1 week)
• Unconstrained optimization: gradient descent and line search methods, trust-region methods, linear and nonlinear least-squares problems. (4 weeks)
• Constrained optimization: optimality conditions and Lagrange multipliers, linear programming and duality, penalties and the Augmented Lagrangian method. (4 weeks)
• Stochastic optimization: stochastic gradient descent and nature-inspired optimization. (2 weeks)
Target Students
Available to Single and Joint Honours Mathematics, Natural Sciences, Liberal Arts, MSc Financial and Computational Mathematics students. Not available to students taking MATH4056.
Classes
You will be taught in a variety of ways including lectures and computer classes.
Assessment
- 20% Coursework 1
- 20% Coursework 2
- 60% Exam 1 (3-hour): Written examination
Assessed by end of autumn semester
Educational Aims
Education 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
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.