Optimization Methods 131891-D
Laboratorium (LAB) Semestr letni 2025/26

Classification of optimization problems and methods. Search space exploration. Analitical and iterative optimization. Necessary and sufficient conditions for extrema of differentiable functionss. Power series expansion. First and second order approximation. Taylor series expansion.

Lab: Introduction to Octave.

Lab: numerical differentiation, numerical gradient and Hessian, numerical first and second order Taylor expansion.

Examples of practical optimization problems: financial leverage optimization, portfolio optimization, TSP and VRP. Computational complexity.

Lab: section methods, line search. Case study: leverage optimization.

Steepest descent and Raphson-Newton method.

Lab: steepest descent and Raphson-Newton method. Case study: portfolio optimization.

Simulated annealing, penalty functions.

Lab: simulated annealing, penalty functions.

Constraint nonlinear optimization. Kuhn-Tucker conditions. Projections. Reduced gradient method.

Lab: reduced gradient method.

Student presentations 1

Student presentations 2

Lab: using external optimization libraries in Octave.

Exam.