Introduction to Optimization

Aim

The course aims to provide a broad introduction to optimization theory and deals with modelling, theory, solution methods and the use of software to solve different types of optimization problems.

Learning objectives:

The course's learning objectives are divided under the following two main headings, and within the framework of these, the learning objectives M1—M6 specify what the student should be able to do after completing the course.

• In mathematical modeling and the use of software to solve optimization problems, be able to:(M1) identify optimization issues and formulate mathematical models of simple optimization problems;(M2) combine knowledge in modeling optimization problems, use of optimization software and programming to solve a given optimization problem, and carry out plausibility assessment and analysis of the result;(M3) give examples of the contexts in which optimization theory can be used and how it can contribute to sustainable development.
• To be able to, within solution methods and theory:use basic concepts and theorems and choose and apply appropriate methods to solve and analyze optimization problems(M4) as modeled with continuous decision variables, and(M5) as modeled with discrete decision variables or in the form of a network, and(M6) which requires a composite optimization method to be usedwithin the scope of what is described by the course content;as part of (M4), (M5) and (M6) clearly report calculations and reasoning, and make simpler plausibility assessments of the results.

Content

Fundamental concepts within optimization, such as mathematical modelling, optimality conditions, convexity, sensitivity analysis, duality, and Lagrangean relaxation. Basic theory and methods for linear and nonlinear optimization, and integer and network optimization.