Optimization

Code:

M4045

Acronym:

M4045

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2016/2017 - 1S

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	21	Official Study Plan since 2013-2014	1	-	6	56	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

Program

Linear Programming. Simplex method
The simplex method in networks.
Dynamic programming (deterministic).
Integer and mixed programming.

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

Introduction to the calculus of variations. Euler-Lagrange formula.

Differential equations depending on controls. State variables and control variables. Presentation of some control problems. The maximum theorem of Pontryagin.

Mandatory literature

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

Teaching methods and learning activities

Teaching using various models in spreadsheets (Excel). Analysis of case studies displayed by students in class.

Other software packages may also be referred to and/or presented (Mathematica, Matlab, Python, ...).

Software

Excel 2010 com add-ins fornecidos pelo docente

keywords

Physical sciences > Mathematics > Applied mathematics

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation	Weight (%)
Participação presencial	0,00
Teste	100,00
Total:	100,00

Eligibility for exams

Distributed evaluation consist in two tests, each totalizing 10 (ten) values to be held during the semester, on dates to be determined. Students will be approved provided they obtain a grade equal or higher than 10 = sum of the total score of the two tests to be held throughout the semester, with a minimum of four (4) values for each test.

Calculation formula of final grade

 

Special assessment (TE, DA, ...)

The tests required under special statutes contain a written test which may be preceded by an oral round, to assess whether the student is in a position of trying to get approved minimum discipline in the written test.

 

Classification improvement

Grade improvement will be made in consideration of the time for appeal.