Course content

First and second order necessary and sufficient (Karush-Kuhn-Tucker) optimality conditions for unconstrained and constrained optimization problems in finite-dimensional vector spaces. Basics of convex analysis and Lagrangian duality theory and their application to optimization problems and algorithms. An overview of modern optimization techniques and algorithms for smooth problems (including line-search/trust-region, quasi-Newton, interior point and active set methods, SQP and augmented Lagrangian approaches). Basic derivative-free and non-smooth optimization methods.

Learning outcome

The student successfully meeting the learning objectives of the course will be able to:
(i) assess the existence and uniqueness of solutions to a given optimization problem;
(ii) validate convexity of functions, sets, and optimization problems;
(iii) derive necessary and sufficient optimality conditions for a given optimization problem;
(iv) solve small optimization problems analytically;
(v) explain the underlying principles and limitations of modern techniques and algorithms for optimization;
(vi) estimate the rate of convergence and complexity requirements of various optimization algorithms;
(vii) implement optimization algorithms on a computer;
(viii) apply optimization algorithms to model problems in engineering and natural sciences.

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 (70%) and the semester assignment (30%). 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. If the course is taught in English, the exam will be given only in English. Students are free to choose Norwegian or English for written assessments.

Recommended previous knowledge

Calculus 1-4, or equivalent.

Course materials

Will be announced at the start of the course.

Credit reductions