2024
Mathematics Programming
Name: Mathematics Programming
Code: MAT10690L
6 ECTS
Duration: 15 weeks/156 hours
Scientific Area:
Mathematics
Teaching languages: Portuguese
Languages of tutoring support: Portuguese
Presentation
The UC aims to prepare students in Non-Linear Optimization topics, complementing the CU Operational Research, allowing them to apply Mathematics in the areas of Economics, Management, Nature Sciences and Engineering.
Sustainable Development Goals
Learning Goals
The curricular unit aims to prepare students in mathematical programming topics, complementing the curricular unit Operational Research, allowing them to investigate in the area of non-linear optimization and apply this knowledge in solving problems in Economics, Management, Natural Sciences and Engineering.
At the end of the u.c. it is intended that students:
- know how to formulate mathematical programming models in various contexts;
- know the main methods (analytical and numerical) for solving mathematical programming problems;
- apply computational tools to solve optimization problems in different areas.
At the end of the u.c. it is intended that students:
- know how to formulate mathematical programming models in various contexts;
- know the main methods (analytical and numerical) for solving mathematical programming problems;
- apply computational tools to solve optimization problems in different areas.
Contents
Non-linear programming. Free optimization and optimization with constraints in the form of equality and inequality. Necessary and sufficient conditions of optimality, Lagrange multipliers, KKT conditions.
Numerical methods of optimization. Free optimization of functions of one and several variables. Constrained optimization: penalty functions, interior point method.
Integer and mixed programming. Multi-objective optimization. Heuristic algorithms.
Formulation of mathematical programming models using the modeling languages (AMPL, MathProg, GAMS, LINGO, etc). Solving the models by software packages. Applications to Economics, Management, Natural Sciences and Engineering.
Numerical methods of optimization. Free optimization of functions of one and several variables. Constrained optimization: penalty functions, interior point method.
Integer and mixed programming. Multi-objective optimization. Heuristic algorithms.
Formulation of mathematical programming models using the modeling languages (AMPL, MathProg, GAMS, LINGO, etc). Solving the models by software packages. Applications to Economics, Management, Natural Sciences and Engineering.
Teaching Methods
The teaching process will be organized based in the form of theoretical and practical-laboratory sessions.
The theoretical sessions are predominantly given on the board and with the projection of slides. The theoretical concepts are illustrated by practical examples. The active participation of students in classes is encouraged.
In the laboratory-practical classes it is foreseen the active use of computational resources and implementation of the most important numerical algorithms.
The theoretical sessions are predominantly given on the board and with the projection of slides. The theoretical concepts are illustrated by practical examples. The active participation of students in classes is encouraged.
In the laboratory-practical classes it is foreseen the active use of computational resources and implementation of the most important numerical algorithms.
Assessment
Students can opt for continuous assessment or the final exam.
The continuous evaluation is privileged and it includes a written test (50%), individual or group work with public presentation (30%) and resolution of exercises by computational tools during practical classes (20%).
At the evaluation by exam, it may be necessary to use computational tools to solve some questions.
To obtain approval for the UC, the student must have at least 10 values in the final grade.
The continuous evaluation is privileged and it includes a written test (50%), individual or group work with public presentation (30%) and resolution of exercises by computational tools during practical classes (20%).
At the evaluation by exam, it may be necessary to use computational tools to solve some questions.
To obtain approval for the UC, the student must have at least 10 values in the final grade.
Teaching Staff (2023/2024 )
- Luís Alberto Godinho Coelho
- Vladimir Alekseevitch Bushenkov [responsible]
