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Continuous Optimization

  • Number of credits 7.5 credits
  • Level Bachelor's level
  • Starting Autumn Term 2024

About the course

Element 1 (4.5 hp) Theory
This part contains theory for nonlinear optimization. The course starts with a discussion of basic notions like classification of optimization problems, objective functions, constraints, feasible solutions, optimal solutions. Then fundamental convexity theory is addressed. A general optimization algorithm is defined, and notions like convergence rate, line search, descent- and ascent directions and optimality conditions are discussed. Optimality conditions for free optimization problems are introduced, and Newton's method for free optimization problems is studied. Next, optimization problems with constraints, Lagrange functions and Lagrange multipliers are defined, and optimility conditions (The Karush-Kuhn-Tucker conditions) are introduced. The duality concept and weak and strong duality theorems are discussed. Finally, some mathematical modeling examples leading to optimization problems are discussed.

Element 2 (3 hp) Computer labs
This part contains implementation of some approximation methods for free optimization problems (steepest descent, quasi-Newton method), and constrained optimization problmes (feasible-point methods, the SQP method). Furthermore, one assignment includes both mathematical modeling, formulation of an optimization model and finding an approximate solution of the model with suitable software.

Application and eligibility

Continuous Optimization, 7.5 credits

Visa tillfällen för föregående termin Autumn Term 2024 Det finns inga senare terminer för kursen


2 September 2024


31 October 2024

Study location



English (upon request)

Type of studies

Daytime, 50%

Required Knowledge

The course requires 60 ECTS in Mathematics and Mathematical Statistics or minimum 120 ECTS and in both cases courses in Multivariable Calculus and Differential Equations minimum 7,5 ECTS and a basic course in computer programming or equivalent.Proficiency in English equivalent to the level required for basic eligibility for higher studies. Where the language of instruction is Swedish, applicants must prove proficiency in Swedish to the level required for basic eligibility for higher studies.


Guaranteed place Applicants in some programs at Umeå University have guaranteed admission to this course. The number of places for a single course may therefore be limited.

Application code



Please note: This application round is intended only for applicants within the EU/EEA and Switzerland. Online application service in Swedish will open 15 March 2024 at 13:00 CET. Application deadline is 15 April 2024. How to apply

Application and tuition fees

As a citizen of a country outside the European Union (EU), the European Economic Area (EEA) or Switzerland, you are required to pay application and tuition fees for studies at Umeå University.

Application fee

SEK 900

Tuition fee, first instalment

SEK 17,850

Total fee

SEK 17,850

Contact us

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Contactperson for the course is:
Study counselor Lars-Daniel Öhman