Course syllabus - Optimization

Objectives

The aim of this advanced course is to give the students insights into basic optimization theory and ability to master efficient algorithms and numerical methods for solving all major classes of optimization problems.

Learning outcomes

At the end of the course the student is expected to be able to

- identify optimization problems and classify them according to their properties
- construct mathematical models of such common types of optimization problems which are mentioned under the headline "Course content" including models for optimization of environmental problems
- define and formulate, for any of the optimization problems treated in the course, suitable numerical methods to solve the problem
- implement numerical solution in Matlab and analyze the performance of the numerical method

Course content

- Linear programming (LP): brief summary of the theory and algorithms LP models such as asset/liability cash flow matching, short term financing; capital budgeting problem
- Solution of nonlinear equations
- Model computation of internal rate of return
- Nonlinear programming: theory and algorithms for unconstrained and constrained optimization, quadratic models, portfolio optimization.
- Statistical models: Maximum likelihood estimation
- Linear and nonlinear parameter estimation: theory and algorithms, models, power system analysis, volatility estimation
- Application examples: defining, setting up, solving and analyzing results from optimization models from mathematical finance, statistics and power system analysis
- Practical solution of optimization problems in Matlab using the Optimization Toolbox and self implemented methods
Models for optimisation of problems related to environmental issues

Tuition

Lectures include theory, problem solving and applications. Exercises are intended to give individual training in problem solving. A laboratory course with emphasis on implementation of numerical algorithms and the use of MATLAB optimization Toolbox.

Specific requirements

At least totally 120 credits in the engineering, natural sciences, business administration or economics areas including Numerical Methods with MATLAB, 7.5 credits, Basic Calculus Continuation Course, 7.5 credits, and Operations Research, 7.5 credits, or equivalent.
In addition Swedish course 3/Swedish course B and English course 6/English course A are required. For courses given entirely in English exemption is made from the requirement in Swedish course 3/Swedish course B.

Examination

Laboratory work, exercises (LAB1), 1.5 credits, marks Pass (G)
Written and/or oral examination (TEN1), 6 credits, marks 3, 4 or 5

A student who has a certificate from MDU regarding a disability has the opportunity to submit a request for supportive measures during written examinations or other forms of examination, in accordance with the Rules and Regulations for Examinations at First-cycle and Second-cycle Level at Mälardalen University (2020/1655). It is the examiner who takes decisions on any supportive measures, based on what kind of certificate is issued, and in that case which measures are to be applied.

Suspicions of attempting to deceive in examinations (cheating) are reported to the Vice-Chancellor, in accordance with the Higher Education Ordinance, and are examined by the University’s Disciplinary Board. If the Disciplinary Board considers the student to be guilty of a disciplinary offence, the Board will take a decision on disciplinary action, which will be a warning or suspension.

Grade

Pass with distinction, Pass with credit, Pass, Fail