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 labs.

The course consists of two parts:
Part 1, theory, 4.5 credits
Part 2, practice, 3 credits

Expected learning outcomes

Knowledge and understanding
After having completed the course the student will be able to:

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

Skills and abilities
After having completed the course the student will be able to:

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

Values and attitudes
After having completed the course the student should be able to:

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

Required Knowledge

Univ: To be admitted you must have (or equivalent) 90 ECTS-credits including 60 ECTS-credits in Computing Science or two years of completed studies within a study programme (120 ECTS-credits). In both cases, the studies must include at least 15 ECTS-credits within Calculus, 7.5 ECTS-credits in Linear Algebra, at least 7.5 ECTS-credits within Programming methodology, at least 4.5 ECTS-credits within Scientific computing/Numerical Analysis, and at least 7.5 ECTS-credits within Matrix computations.

Proficiency in English equivalent to Swedish upper Secondary course English A/5. Where the language of instruction is Swedish, applicants must prove proficiency in Swedish 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 three mandatory assignments that results 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 rated G/passed when all three mandatory assignments are assessed as completed. If a student participates in the examination but do not get all assignments assessed as completed at the end of the course, the grade U is given on the part.

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 final grade of the course is a summary assessment of the results and is usually the same as the grade of part 1 and is never lower than that grade.

For all students who do not pass the regular examination there are additional opportunities to do the examination.

A student who has passed an examination may not be re-examined.

A student who has taken two tests for a course or a segment of a course, without passing, has the right to have another examiner appointed, unless there exist special reasons (Higher Education Ordnance Chapter 6, Section 22). Requests for new examiners are made to the head of the Department of Computing Science.

Examination based on this syllabus is guaranteed for two years after the first registration of the course. This applies even if the course is closed down and this syllabus ceased to be valid.

TRANSFER OF CREDITS
Students have the right to be tried on prior education or equivalent knowledge and skills acquired in the profession can be credited for the same education at Umeå University. Application for credit is submitted to the Student Services / Degree. For more information on credit transfer available at Umeå University's student web, www.student.umu.se, and the Higher Education Ordinance (Chapter 6). A refusal of crediting can be appealed (Higher Education chapter 12) to the University Appeals Board. This applies to the whole as part of the application for credit transfer is rejected.

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.

Course connections to programs and degrees
The course is a mandatory course for the Master's Programme in Computational Science and Engineering.