Optimization

Code:

M.IA030

Acronym:

O

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2025/2026 - 2S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Master in Artificial Intelligence

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
M.IA	3	Syllabus	1	-	6	39	162

Teaching language

Suitable for English-speaking students

Objectives

The course aims to introduce n aa rigorous the optimization theory (linear and nonlinear), variational calculus and theory of control. The fundamental concepts of these areas are addressed, as well as the most important mathematical tools for its analysis.

 

Learning outcomes and competences

The aim is for students to acquire skills in algorithmic modeling and solving real situations common in many scientific and economic activities.

 

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Basic knowledge of Linear Algebra (matrices, vector spaces) and Calculus of functions of several real variables.

Program

Linear optimization problems.
Non-linear optimization problems.
Problems with and without constraints.

Calculus of variations.

Differential equations depending on controls. State variables and control variables. Presentation of some control problems. Pontryagin's maximum principle.

Mandatory literature

Krasnov M. L.; Cálculo variacional
Smirnov Gueorgui; Curso de optimização. ISBN: 972-592-175-5
Jensen Paul A.; Operations research. ISBN: 0-471-38004-0
Levi Mark 1951-; Classical mechanics with calculus of variations and optimal control. ISBN: 9780821891384
Pontriaguine L.; Théorie mathématique des processus optimaux
Mokhtar S. Bazaraa; Linear programming and network flows. ISBN: 0-471-06015-1

Teaching methods and learning activities

Presentation of UC subjects and scientific discussion with students

Software

Matlab
Python

keywords

Physical sciences > Mathematics > Applied mathematics

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation	Weight (%)
Apresentação/discussão de um trabalho científico	40,00
Exame	50,00
Participação presencial	10,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	116,00
Frequência das aulas	42,00
Apresentação/discussão de um trabalho científico	4,00
Total:	162,00

Eligibility for exams

Unconditional.

Calculation formula of final grade

40% - Written work and presentation.



10% - In-person participation



50% - Exam

Special assessment (TE, DA, ...)

50% - A new written work and presentation.



50% - Exam

Classification improvement

50% - A new written work and presentation.



50% - Appeal exam