Optimization

Code:

M532

Acronym:

M532

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2015/2016 - 2S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Doctoral Program in Mathematics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
IUD-M	5	PE do Prog Inter-Univ Dout Mat	1	-	9	60	243

Teaching language

English

Objectives

This course aims to introduce the students to the essential concepts of optimization, with a special emphasis on convex optimization. Additionally it will approach some of the recent developments in the area, bringing the students closer to current topics of research in the area.

Learning outcomes and competences

The following skills are to be developed: critical thinking, mastery over the basic concepts of optimization, problem solving, the use of computational software for optimization problems.

Working method

Presencial

Program

1 - Optimality conditions and duality theory for conic, convex and non linear optimization.
2 - Numerical methods for continuous optimization.
3 - Semidefinite methods and representability in polynomial optimization.
4 - Continuous relaxations for combinatorial problems.

Mandatory literature

Boyd Stephen; Convex optimization. ISBN: 0-521-83378-3
Borwein Jonathan M.; Convex analysis and nonlinear optimization. ISBN: 0-387-98940-4

Complementary Bibliography

Beck, Amir; Introduction to Nonlinear Optimization, MOS-SIAM, 2014. ISBN: 978-1-611973-64-8

Teaching methods and learning activities

The lectures will be of a mostly theoretical nature and will include examples and exercises allowing the application of aquired knowledge. Throughout the semester help will be available to the students for problem solving and exam preparation.

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	60,00
Trabalho escrito	40,00
Total:	100,00

Calculation formula of final grade

Final grade = 0.6*EG + 0.4*PG
where EG is the exam grade and PG is the average grade in the problem sets.