Computer Engineering MA, Applied Optimization, 6 credits

Aim

The course aims to provide knowledge about optimization and how it is used in practical applications in areas such as information technology (machine learning, robotics, algorithms and complexity), communication networks, economics, signal processing, and information theory.

Course objectives

After the course the student should be able to
- formulate an optimization problem with constraints.
- apply the Karush-Kuhn-Tucker conditions for optimization with constraints.
- explain different optimization algorithms for linear and non-linear problems without and with constraints, and when they are applicable.
- describe how non-convex optimization problems can be reformulated into convex problems, and in cases when non-convex optimization problems can be reformulated to these.
- describe regularization methods for solving ill-posed problems, and when they are applicable.
- apply and program optimization algorithms for problem solving.
- evaluate the suitability of different optimization algorithms for an optimization problem.

Content

Fundamental optimization concepts, duality, necessary and sufficient conditions, graphical solutions.
Convex sets, functions and optimization problems, reformulation into convex problems.
Linear programming: the simplex method, sensitivity analysis.
Non-linear programming: optimization methods for non-linear problems without and with constraints.
Heuristic methods for searching for global optimum.
Regularization for ill-posed problems: Tikhonov regularization, different norms.
Examples of signal processing, statistics, machine learning, radio resource allocation, production planning, economics and game theory will be dealt with depending on the participants' background and interest.

Entry requirements

Computer Engineering BA (ABC), 30 credits, including 6 credits in programming. Mathematics BA (A), 22.5 credits, including Mathematical Statistics, 6 credits and 6 credits Linear Algebra.

Selection rules and procedures

The selection process is in accordance with the Higher Education Ordinance and the local order of admission.

Teaching form

Teaching is carried out by means of lectures, seminars and labs.

Examination form

I102: Assigments and Labs, 3 Credits
Grade scale: Fail (U) or Pass (G)

T102: Exam, 3 Credits
Grade scale: Seven-grade scale, A, B, C, D, E, Fx and F. Fx and F represent fail levels.

Grading criteria for the subject can be found at www.miun.se/GradingCriteria

The examiner has the right to offer alternative examination arrangements to students who have been granted the right to special support by Mid Sweden University’s disabilities adviser.

If examination on campus cannot be conducted according to decision by the vice-chancellor, or whom he delegated the right to, the following applies: Exam T102, will be replaced with two parts, online examination and follow-up. Within three weeks of the online examination, a selection of students will be contacted and asked questions regarding the examination. The follow-up consists of questions concerning the execution of the on-line exam and the answers that the student have submitted.

Grading system

Seven-grade scale, A, B, C, D, E, Fx and F. Fx and F represent fail levels.