2026

Optimization and Optimal Control

Name: Optimization and Optimal Control
Code: MAT11694D
6 ECTS
Duration: 15 weeks/156 hours
Scientific Area: Mathematics

Teaching languages: Portuguese
Languages of tutoring support: Portuguese

Presentation

The purpose of this course is to transfer mathematical knowledge that can be developed and implemented in a professional context,
business, research or teaching.

Sustainable Development Goals

Learning Goals

This course aims to consolidate and develop knowledge of the theory and numerical methods of
optimization. An emphasis will be done on the problems of optimization of dynamic systems (dynamic
programming, optimal control) and on more recent numerical algorithms. To foster students' abilities in
applying optimization methods in practical tasks, the optimization software (Lingo, Matlab, etc..) will be
used.

Contents

Mathematical modelling and optimization. Classification of optimization problems.
Theory and algorithms for unconstrained optimization.
Theory and algorithms for constrained optimization.
Heuristic, evolutionary and genetic algorithms. Global optimization. Multiobjective optimization.
Ill-posed optimization problems and their regularization.
Optimization of dynamic systems. Optimal control. Pontriagin’s principle of maximum. Applications.
Automatic differentiation. Dynamic programming.
Computational implementation of optimization methods.

Teaching Methods

Lectures and tutoring, with each student being responsible for reading the bibliography advised by the
teacher. For some topics there may be seminars focused in specific points of the course program.
Evaluation: practical works during the semester and an individual project, with final discussion.