The course deals with algorithms and fundamental theory for nonlinear finite-dimensional optimization problems. Fundamental optimization concepts, such as convexity and duality are also introduced.
The main focus is nonlinear programming, unconstrained and constrained. Areas considered are unconstrained minimization, linearly constrained minimization and nonlinearly constrained minization. The focus is on methods which are considered modern and efficient today.
Linear programming is treated as a special case of nonlinear programming.
Semidefinite programming and linear matrix inequalities are also covered.
That the student should obtain a deep understanding of the mathematical theory and the numerical methods for nonlinear programming.
After completed course, the student should be able to
Derive optimality conditions for different classes of nonlinear optimization problems.
Explain how the method of steepest descent, the method of conjugate gradients, quasi-Newton methods and Newton methods work for unconstrained optimization, both linesearch methods and trust-region methods
Explain methods related to the above for equality-constrained problems
Explain methods related to the above for inequality-constrained problems
Explain how interior methods for semidefinite programming work
