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IB352-15 Applied Optimization Methods

Department
Warwick Business School
Level
Undergraduate Level 3
Module leader
Juergen Branke
Credit value
15
Module duration
10 weeks
Assessment
30% coursework, 70% exam
Study location
University of Warwick main campus, Coventry
Introductory description

To introduce general algorithms for convex and non-convex 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 web page

Module aims

To introduce general algorithms for convex and non-convex 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, calculus-derivatives, 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.
Multi-objective 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 non-linear 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/add-on optimization solver.

Transferable skills

Distinguish between convex and non-convex 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


  • Answerbook Pink (12 page)
  • Students may use a calculator
  • Graph paper
Feedback on assessment

For the assignment, students will receive individual feedback. For the exam, general feedback will be provided about typical errors made.

Past exam papers for IB352

Courses

This module is Core for:

  • USTA-G300 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)
  • USTA-G301 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:

  • UCSA-G4G1 Undergraduate Discrete Mathematics
    • Year 3 of G4G1 Discrete Mathematics
    • Year 3 of G4G1 Discrete Mathematics
  • Year 3 of UCSA-G4G3 Undergraduate Discrete Mathematics
  • Year 4 of UCSA-G4G2 Undergraduate Discrete Mathematics with Intercalated Year
  • UECA-4 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
  • USTA-G300 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 UMAA-G1NC Undergraduate Mathematics and Business Studies
  • Year 4 of UECA-GL12 Undergraduate Mathematics and Economics (with Intercalated Year)
  • USTA-G1G3 Undergraduate Mathematics and Statistics (BSc MMathStat)
    • Year 3 of G1G3 Mathematics and Statistics (BSc MMathStat)
    • Year 4 of G1G3 Mathematics and Statistics (BSc MMathStat)
  • USTA-G1G4 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:

  • UPHA-V7ML 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 USTA-G300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
  • USTA-G301 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
  • USTA-Y602 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 USTA-Y603 Undergraduate Mathematics,Operational Research,Statistics,Economics (with Intercalated Year)

This module is Option list B for:

  • Year 4 of UCSA-G504 MEng Computer Science (with intercalated year)
  • UCSA-G500 Undergraduate Computer Science
    • Year 3 of G500 Computer Science
    • Year 3 of G500 Computer Science
  • UCSA-G502 Undergraduate Computer Science (with Intercalated Year)
    • Year 4 of G502 Computer Science with Intercalated Year
    • Year 4 of G502 Computer Science with Intercalated Year
  • UCSA-G503 Undergraduate Computer Science MEng
    • Year 3 of G500 Computer Science
    • Year 3 of G503 Computer Science MEng
    • Year 3 of G503 Computer Science MEng
  • USTA-GG14 Undergraduate Mathematics and Statistics (BSc)
    • Year 3 of GG14 Mathematics and Statistics
    • Year 3 of GG14 Mathematics and Statistics
  • Year 4 of USTA-GG17 Undergraduate Mathematics and Statistics (with Intercalated Year)

This module is Option list C for:

  • Year 4 of UCSA-G504 MEng Computer Science (with intercalated year)
  • UCSA-G500 Undergraduate Computer Science
    • Year 3 of G500 Computer Science
    • Year 3 of G500 Computer Science
  • UCSA-G502 Undergraduate Computer Science (with Intercalated Year)
    • Year 4 of G502 Computer Science with Intercalated Year
    • Year 4 of G502 Computer Science with Intercalated Year
  • UCSA-G503 Undergraduate Computer Science MEng
    • Year 3 of G500 Computer Science
    • Year 3 of G503 Computer Science MEng
    • Year 3 of G503 Computer Science MEng
  • USTA-G300 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:

  • UPHA-V7ML 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)