Optimization

Code:

M4045

Acronym:

M4045

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2023/2024 - 2S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Master in Mathematical Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
M:ENM	11	Official Study Plan since 2023/2024	1	-	6	48	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

Exposition and discussion of the main subjects of the UC.

Selected group of exercises to be addressed by the students.

Software

Matlab
Python

keywords

Physical sciences > Mathematics > Applied mathematics

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation	Weight (%)
Teste	100,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	110,00
Frequência das aulas	52,00
Total:	162,00

Eligibility for exams

Unconditional.

Calculation formula of final grade

Final classification = T1 + T2
T1 = classification of the 1st test, with a score of 10 values
T2 = classification of the 2nd test, with a score of 10 values

Special assessment (TE, DA, ...)

The same evaluation criteria is used for all students.

Classification improvement

Grade improvement will be made in the appeal examination.

Observations

Students with a grade of at least 18 may be asked to take an additional exam to confirm their grade. Students with a grade of 8 or 9 may also be invited to take an additional exam as an opportunity to the grade of 10.