IB35215 Applied Optimization Methods
Introductory description
To introduce general algorithms for convex and nonconvex optimization problems arising in various application areas such as financial portfolio optimization, energy system planning, and engineering design optimization, and their computational aspects using a numerical software tool such as Matlab.
Module aims
To introduce general algorithms for convex and nonconvex optimization problems arising in various application areas such as financial portfolio optimization, energy system planning, and engineering design optimization, and their computational aspects using a numerical software tool such as Matlab.
Outline syllabus
This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.
Module introduction with examples of several optimization problems in various application areas such as financial portfolio optimization, energy system planning, and engineering design optimization, and review of mathematical background materials (linear algebra, calculusderivatives, etc.).
Introduction to a software for modelling and solving optimization problems.
Optimality conditions.
Unconstrained optimization.
Quadratic programming.
Constrained optimization.
Discrete optimization and exact methods.
Heuristics.
Global optimization.
Multiobjective optimization.
We plan to cover various applications such as financial portfolio optimization, energy system planning, and engineering design optimization, and several solution algorithms.
Learning outcomes
By the end of the module, students should be able to:
 Derive general optimality conditions for convex optimization problems.
 Apply numerical algorithms for unconstrained and constrained convex optimization problems.
 Apply exact methods for discrete optimization problems with general nonlinear convex objective as well heuristics methods.
 Understand global optimization methods.
Indicative reading list
 G. Calafiore and L. El Ghaoui, Optimization Models, Cambridge Publications, 2014
 P. Venkataraman, Applied Optimization with Matlab Programming, Wiley, 2nd Edition, 2009
 J. Nocendal and S. Wright, Numerical Optimization, Springer, 2nd Edition, 2000
 C. Papadimitriou and K. Steiglitz, Combinatorial Optimization: Algorithms and Complexity, Dover Publications, 1998
 A. E. Eiben and J. E. Smith, Introduction to Evolutionary Computing, Springer 2015
Subject specific skills
Use Matlab or similar numerical software to solve optimization problems using numerical algorithms and builtin/addon optimization solver.
Transferable skills
Distinguish between convex and nonconvex optimization problems and different solution techniques.
Study time
Type  Required 

Lectures  20 sessions of 1 hour (26%) 
Tutorials  10 sessions of 1 hour (13%) 
Private study  48 hours (62%) 
Total  78 hours 
Private study description
Private Study.
Costs
No further costs have been identified for this module.
You do not need to pass all assessment components to pass the module.
Assessment group D3
Weighting  Study time  

Group Work  25%  18 hours 
Numerical problem solving. 

Weekly Online Multiple Choice Questions  5%  4 hours 
Online Examination  70%  50 hours 
Exam ~Platforms  AEP

Feedback on assessment
For the assignment, students will receive individual feedback. For the exam, general feedback will be provided about typical errors made.
Courses
This module is Core for:

USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
 Year 3 of G30C Master of Maths, Op.Res, Stats & Economics (Operational Research and Statistics Stream)
 Year 3 of G30C Master of Maths, Op.Res, Stats & Economics (Operational Research and Statistics Stream)

USTAG301 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated
 Year 3 of G30G Master of Maths, Op.Res, Stats & Economics (Operational Research and Statistics Stream) Int
 Year 4 of G30G Master of Maths, Op.Res, Stats & Economics (Operational Research and Statistics Stream) Int
This module is Optional for:

UCSAG4G1 Undergraduate Discrete Mathematics
 Year 3 of G4G1 Discrete Mathematics
 Year 3 of G4G1 Discrete Mathematics
 Year 3 of UCSAG4G3 Undergraduate Discrete Mathematics
 Year 4 of UCSAG4G2 Undergraduate Discrete Mathematics with Intercalated Year

UECA4 Undergraduate Economics 4 Year Variants
 Year 4 of LV16 Economics & Economic History with Study Abroad
 Year 4 of L114 Industrial Economics with Study in Europe

USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
 Year 3 of G300 Mathematics, Operational Research, Statistics and Economics
 Year 4 of G300 Mathematics, Operational Research, Statistics and Economics
 Year 3 of UMAAG1NC Undergraduate Mathematics and Business Studies
 Year 4 of UECAGL12 Undergraduate Mathematics and Economics (with Intercalated Year)

USTAG1G3 Undergraduate Mathematics and Statistics (BSc MMathStat)
 Year 3 of G1G3 Mathematics and Statistics (BSc MMathStat)
 Year 4 of G1G3 Mathematics and Statistics (BSc MMathStat)

USTAG1G4 Undergraduate Mathematics and Statistics (BSc MMathStat) (with Intercalated Year)
 Year 4 of G1G4 Mathematics and Statistics (BSc MMathStat) (with Intercalated Year)
 Year 5 of G1G4 Mathematics and Statistics (BSc MMathStat) (with Intercalated Year)
This module is Unusual option for:

UPHAV7ML Undergraduate Philosophy, Politics and Economics
 Year 3 of V7ML Philosophy, Politics and Economics (Tripartite)
 Year 3 of V7ML Philosophy, Politics and Economics (Tripartite)
 Year 3 of V7ML Philosophy, Politics and Economics (Tripartite)
This module is Option list A for:
 Year 3 of USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics

USTAG301 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated
 Year 3 of G30E Master of Maths, Op.Res, Stats & Economics (Actuarial and Financial Mathematics Stream) Int
 Year 4 of G30E Master of Maths, Op.Res, Stats & Economics (Actuarial and Financial Mathematics Stream) Int

USTAY602 Undergraduate Mathematics,Operational Research,Statistics and Economics
 Year 3 of Y602 Mathematics,Operational Research,Stats,Economics
 Year 3 of Y602 Mathematics,Operational Research,Stats,Economics
 Year 4 of USTAY603 Undergraduate Mathematics,Operational Research,Statistics,Economics (with Intercalated Year)
This module is Option list B for:
 Year 4 of UCSAG504 MEng Computer Science (with intercalated year)

UCSAG500 Undergraduate Computer Science
 Year 3 of G500 Computer Science
 Year 3 of G500 Computer Science

UCSAG502 Undergraduate Computer Science (with Intercalated Year)
 Year 4 of G502 Computer Science with Intercalated Year
 Year 4 of G502 Computer Science with Intercalated Year

UCSAG503 Undergraduate Computer Science MEng
 Year 3 of G500 Computer Science
 Year 3 of G503 Computer Science MEng
 Year 3 of G503 Computer Science MEng

USTAGG14 Undergraduate Mathematics and Statistics (BSc)
 Year 3 of GG14 Mathematics and Statistics
 Year 3 of GG14 Mathematics and Statistics
 Year 4 of USTAGG17 Undergraduate Mathematics and Statistics (with Intercalated Year)
This module is Option list C for:
 Year 4 of UCSAG504 MEng Computer Science (with intercalated year)

UCSAG500 Undergraduate Computer Science
 Year 3 of G500 Computer Science
 Year 3 of G500 Computer Science

UCSAG502 Undergraduate Computer Science (with Intercalated Year)
 Year 4 of G502 Computer Science with Intercalated Year
 Year 4 of G502 Computer Science with Intercalated Year

UCSAG503 Undergraduate Computer Science MEng
 Year 3 of G500 Computer Science
 Year 3 of G503 Computer Science MEng
 Year 3 of G503 Computer Science MEng

USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
 Year 4 of G30C Master of Maths, Op.Res, Stats & Economics (Operational Research and Statistics Stream)
 Year 4 of G30C Master of Maths, Op.Res, Stats & Economics (Operational Research and Statistics Stream)
This module is Option list G for:

UPHAV7ML Undergraduate Philosophy, Politics and Economics
 Year 2 of V7ML Philosophy, Politics and Economics (Tripartite)
 Year 2 of V7ML Philosophy, Politics and Economics (Tripartite)
 Year 2 of V7ML Philosophy, Politics and Economics (Tripartite)