Engineering Optimization, 7.5 Credits

Contents

The course deals with theory and algorithms for optimization of nonlinear problems, something that is common in a number of applications. The course deals with problem formulations both with and without non-linear constraints, which gives a great freedom in how problems can be formulated and solved. Together, this gives the students access to very powerful tools for solving many important problems. The course deals with various optimization efforts and algorithms, theory of nonlinear problems, conditions for optimum, convergence rate, sensitivity analysis and least-square problems. Furthermore, the course deals with how these skills are used in two or three selected applications, such as geometric measurement problems and design optimization. Skills training and increased understanding are acquired through computer assignments.

The course consists of two parts:

• Part 1, theory, 4.5 credits
• Part 2, problem solving, 3 credits

Expected learning outcomes

Knowledge and understanding
After completing the course, the student should be able to:

• (FSR 1) define fundamental concepts within optimization, e.g. minimizer, convergence, objective function, termination conditions, descent,
• (FSR 2) explain the optimal conditions for continuous problems with and without constraints,
• (FSR 3) explain the underlying ideas behind important optimization algorithms, e.g. steepest descent, Newton's method, barrier methods,
• (FSR 4) explain the underlying ideas behind techniques to ensure convergence, e.g. line search and trust region.

Competence and skills
After completing the course, the student should be able to:

• (FSR 5) implement an objective function, constraints and other necessary functions to solve a given optimization problem numerically,
• (FSR 6) implement a given optimization algorithm,
• (FSR 7) reformulate an application problem to a mathematical optimization problem,
• (FSR 8) solve given optimization problems with and without constraints.

Judgement and approach
After completing the course, the student should be able to:

• (FSR 9) assess different optimization algorithms for a given problem and decide the suitability of them,
• (FSR 10) critically evaluate practical results and compare them with theoretical expectations.

Required Knowledge

At least 90 ECTS, including 60 ECTS Computing Science, or 120 ECTS within a study programme. At least 7.5 ECTS programming; 7.5 ECTS linear algebra; 7.5 ECTS numerical linear algebra; 15 ECTS differential and integral calculus; and 4.5 ECTS numerical analysis. Proficiency in English equivalent to the level required for basic eligibility for higher studies.

Form of instruction

Education consists of lectures, classroom exercises in smaller groups, and mandatory assignments. In addition to scheduled activities, individual work with the material is required.

Examination modes

The examination of Part 1 (FSR 1-5, FSR 7-10) consists of a written exam in halls. The grades given are Fail (U), Pass (3), Pass with Merit (4), or Pass with Distinction (5).

The examination of Part 2 (FSR 5-7, 9-10) consists of assignments that result in written reports. The assignments usually contain both theoretical and practical parts. The assignments are assessed as either complete or uncomplete. In part 2, the grades given are Passed (G) or Fail (U). The part will be graded G when all mandatory assignments are assessed as completed.

On the course as a whole, the grades given are Fail (U), Pass (3), Pass with Merit (4), or Pass with Distinction (5). In order to pass the course, both mandatory parts must be passed. The grade on the course is determined by the grade on Part 1.

Adapted examination
The examiner can decide to deviate from the specified forms of examination. Individual adaptation of the examination shall be considered based on the needs of the student. The examination is adapted within the constraints of the expected learning outcomes. A student that needs adapted examination shall no later than 10 days before the examination request adaptation from the Department of Computing Science. The examiner makes a decision of adapted examination and the student is notified.

Other regulations

This course may not be used towards a degree, in whole or in part, togehter with another course of similar content. If in doubt, consult the student counselors at the Department of Computing Science and / or the program director of your program.

In particular, this course can not, in whole or in part, be used in a degree together with 5DA001 Non-linear optimazation. The overlap between these two courses are 5 credits.

If the syllabus has expired or the course has been discontinued, a student who at some point registered for the course is guaranteed at least three examinations (including the regular examination) according to this syllabus for a maximum period of two years from the syllabus expiring or the course being discontinued.