Modelling and Optimization

Code:

M3023

Acronym:

M3023

Level:

300

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2022/2023 - 1S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Artificial Intelligence and Data Science

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:IACD	1	study plan from 2021/22	3	-	6	56	162

Teaching language

Suitable for English-speaking students

Objectives

The main objective of the course is to introduce rigorously the main concepts of optimization and its applications. Those concepts and the relevant mathematical tools to their analysis will be considered in the course.

Learning outcomes and competences

To acquire the main concepts of optimization, skills in algorithmic modeling and solving real situations common in many scientific and economic activities.

Working method

Presencial

Program

First concepts. Models, examples and applications of Linear Programming (LP), integer programming (IP), Binary and Mista (PIM).   

Use of python in linear programming.

Minimizing or maximizing functions. Applications in python.

Nonlinear optimization. Theoretical concepts of duality.

Uni-dimensional optimization methods.
Methods of comparison of network points methods.
Method of bisection method.
Method of the golden section methods.
Free and restricted optimization.
Methods of descent methods.
General scheme of descent methods. Linear search.
The gradient method.
Newton's method.
Conjugate direction methods.
Conjugate direction methods for quadratic functions.

Mandatory literature

Igor Griva; Linear and nonlinear optimization. ISBN: 978-0-898716-61-0
Eligius M. T. Hendrix; Introduction to nonlinear and global optimization. ISBN: 978-0-387-88669-5
Press William H. 070; Numerical recipes. ISBN: 0-521-30811-9

Complementary Bibliography

Jensen Paul A.; Operations research. ISBN: 0-471-38004-0
N. S. Bakhvalov; Numerical methods

Teaching methods and learning activities

Classroom teaching with the use of various models in in python (packages numpy and scipy). Analysis of case studies exposed in class.

Software

python

keywords

Physical sciences > Mathematics > Applied mathematics > Numerical analysis
Physical sciences > Mathematics > Applied mathematics > Operations research

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation	Weight (%)
Teste	85,00
Trabalho prático ou de projeto	15,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	106,00
Frequência das aulas	56,00
Total:	162,00

Eligibility for exams

No frequency requirements are required.

Calculation formula of final grade

Final classification = t1 + t2 + tc
t1 = 1st test score quoted to 8,5
t2 = 2st test score quoted to 8,5
tc = computational work quoted to 3

NOTE: tc is obtained during class time.

SECOND SEASON EXAM:
Final classification = er1 + er2 + tc
er1 = 1st exam score quoted to 8,5
er2 = 1st exam score quoted to 8,5
tc   = obtained during class time.

(1) The second season exam consists of two parts corresponding to the division of matter for the tests.

(2) In the second season exam, the student can choose one or two of its parts. If he/she submits it for correction, it will replace the corresponding classification(s) obtained in the test(s).