Course content

Finite dimensional theory for extrema with and without constraints. Convexity. Brief review of linear optimization and duality. Functionals, functional derivatives, and variational calculus. Central algorithms and applications.

Learning outcome

1. Knowledge. The student masters the theory of existence and uniqueness for finite dimensional optimization problems with or without constraints. The student has knowledge of basic analytical and numerical techniques for optimization, with an emphasis on mathematical understanding. The student is also familiar with basic principles of the calculus of variations, i.e. the optimization of functionals on function spaces.

2. Skills. The student masters convexity. The student can solve simple finite dimensional optimization problems analytically, and larger or more complex problems numerically. The student is able to formulate concrete problems as variational problems with or without constraints, and to derive the associated Euler-Lagrange equations.

Learning methods and activities

Lectures, exercises and semester assignment. Portfolio assessment is the basis for the grade awarded in the course. This portfolio comprises a written final examination (80%) and the semester assignment (20%). The results for the constituent parts are to be given in %-points, while the grade for the whole portfolio (course grade) is given by the letter grading system. Retake of examination may be given as an oral examination. Lectures will be given in English if international master or exchange students want to attend the course.

Recommended previous knowledge

The course is based on the courses Calculus 1-4, or equivalent. TMA4145 Linear methods, or equivalent.

Course materials

Will be announced at the start of the course.

Credit reductions