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Applied Optimization

6 ECTS
Master's
Czech
Michal Černý

The aim of the course is to introduce students to optimization methods and their use in operations research. Students will be introduced to the formulation of a range of real-world problems leading to linear, integer or non-linear programming - e.g. problems in process scheduling, transportation and logistics, production management, efficiency evaluation (DEA), classification and data mining, portfolio management, statistical data processing and other areas. They will learn the basic methods of solving optimization problems formulated in this way, both exact and heuristic methods. They will also gain an overview of available optimization solvers.

Course outline

Optimisation problems
Formulation of optimisation problems.
Optimisation
Continuous vs. discrete optimisation, linear vs. nonlinear problems, multi-criteria problems.
Use cases
Problems in transport and logistics, various variants of the TSP.
Process management
Scheduling and process control, job scheduling.
Applications in financial analysis
Financial applications, portfolio management.
DEA
DEA and efficiency evaluation.
Data mining
Applications in classification, data analysis, and data mining.
Basic optimisation algorithms
Overview of algorithms for linear, nonlinear and discrete programming.
Heuristic methods
Heuristic and metaheuristic methods for complex optimisation problems.
Modelling
Modelling languages, solvers, numerical problems, implementation issues.
Computational complexity in optimisation
Computational complexity of optimisation problems.
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