Continuous Optimization

Education facts

Code: 5MA171

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.

Entry requirements

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.

Education offerings

Each offering has its own dates and conditions. Closed offerings are retained as history and do not mean that a new application is open.

• Continuous Optimization

  Umeå University

  Start date: 31 August 2026

  End date: 1 November 2026

  Pace of study: 50 %