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

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 or Swedish level 3 and English course 6 or English level 2 are required. For courses given entirely in English exemption is made from the requirement in Swedish course 3 or Swedish level 3.

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 disability study support, can request adaptions for the examination. It is the examiner who takes decisions on any adaptions, based on the certificate and other conditions.

Grade

Grading scale: 5, 4, 3