Optimization

The lectures will cover concepts, techniques and methods, with a strong focus on practical applications. Computer support will be used to
solve larger problems.
Some classes will be computer-based, encouraging the applied nature of the models and techniques presented, aimed at Management and
Finance problems.
This way, some classes will have theoretical and theoretical-practical components, involving the exposition of concepts, methods and
algorithms, including the resolution of small-scale applied cases. There will also be classes of a more applied nature, in which appropriate
computer tools will be used for the computational resolution of larger applied cases.
Monitoring the learning process with periodic assessments should help the student to consolidate the syllabus elements, both the
theoretical elements and the practical and applied subjects, which should strengthen the know-how acquisition and the students’ autonomy
in the practical use of this knowledge. The aim is also for the students to gain skills that will enable them to discover ways of responding to
new optimisation problems within the scope of the course.

This course introduces mathematical optimisation techniques, using linear, integer linear and non-linear programming models.
Techniques for solving the proposed mathematical models are studied and their application in the fields of Management and Finance is
encouraged, namely in investment project selection problems, investment portfolios, financial flows of assets and liabilities, among others.
In addition to the study of mathematical calculation methods, appropriate software will be used to solve the proposed optimisation models,
including Excel tools and Python libraries.
The aim is to make students aware of the mathematical modelling of the proposed problems. They will also be familiar with techniques for
solving these problems, including solving them using specific computer applications. The aim is thus to provide students with the theoretical
and practical knowledge to apply quantitative techniques to support decision-making.

1 Introduction to mathematical modelling
1.1 Motivation for mathematical optimisation
1.2 Mathematical formulation of problems
2 Linear Programming
2.1 Properties
2.2 Techniques for solving continuous linear formulations
2.3 Duality and optimality conditions
2.4 Sensitivity analysis and economic interpretation of solutions
2.5 Solving continuous linear models using computer programmes
2.6 Applications of linear programming to management and finance
3 Integer linear programming
3.1 Properties
3.2 Modelling techniques using binary variables
3.3 Solving integer linear models using computer programmes
3.4 Applications of integer linear programming to management and finance
4 Non-linear programming
4.1 Properties
4.2 Unconstrained optimisation of real functions with one variable
4.3 Unconstrained optimisation of multivariable real functions
4.4 Optimisation with constraints
4.5 Quadratic programming
4.6 Applications of non-linear programming to management and finance

NAO