Optimization and Applications

Code:

M3013

Acronym:

M3013

Level:

300

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2020/2021 - 2S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Biology

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:B	0	Official Study Plan	3	-	6	56	162
L:CC	8	Plano de estudos a partir de 2014	2	-	6	56	162
			3
L:F	2	Official Study Plan	2	-	6	56	162
			3
L:G	2	study plan from 2017/18	2	-	6	56	162
			3
L:M	46	Official Study Plan	2	-	6	56	162
			3
L:Q	0	study plan from 2016/17	3	-	6	56	162

Teaching language

Suitable for English-speaking students

Objectives

It is intended that students

1. Become familiar with various problems that can be modeled by linear programming (LP), integer programming (IP), binary integer programming (GDP) or mixed (PIM) and nonlinear programming.


2. Acquire skills in modeling and solving algorithmic real situations common in many scientific and economic activities.


3. Become familiar with key theoretical concepts, methods and algorithms of linear programming (LP), integer programming (IP), binary integer programming (GDP) or mixed (PIM) and dynamic programming in particular duality, complementarity, and modeling using Lagrangean flows in Networks and others.


4. To acquire skills in algorithmic modeling and solving real situations common in many scientific and economic activities.

Learning outcomes and competences

To acquire skills in algorithmic modeling and solving real situations common in many scientific and economic activities.

Working method

Presencial

Program

Program planned

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


2. Problems modeled with networks flows - minimum cost problems, maximum flow problem (FM). Problem of the shortest path in a digraph. Others.


3. Introduction to Nonlinear optimization. Applications.


4. Theoretical concepts of duality. Sensitivity. Post-optimal analysis. Examples.


5. Dynamic programming (deterministic). Applications to Genomics.

Mandatory literature

Igor Griva, Stephen G. Nash, Ariela Sofer; Linear and Nonlinear Optimization. ISBN: 978-0-898716-61-0
Frank R. Giordano, William P. Fox, Steven B. Horton; A first course in Mathematical Modeling. ISBN: 978-1-285-05090-4

Complementary Bibliography

Gomes, Diogo; Sernadas, Amílcar; Sernadas, Cristina; Rasga, João; Mateus, Paulo; A mathematical primer on linear optimization, College Publications, London, 2019. ISBN: 978-1-84890-315-9
Jensen Paul A.; Operations research. ISBN: 0-471-38004-0
Eligius M. T. Hendrix; Introduction to nonlinear and global optimization. ISBN: 978-0-387-88669-5

Teaching methods and learning activities

Classroom teaching with the use of various models. Analysis of case studies exposed in class by students.

Evaluation Type

Evaluation with final exam

Assessment Components

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

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	106,00
Frequência das aulas	56,00
Apresentação/discussão de um trabalho científico
Elaboração de projeto
Total:	162,00

Eligibility for exams

Final classification equal to or greater than 9,5.

Calculation formula of final grade

The exam score of 0-20 with a possible bonus up to a maximum of 2 values through optional written work and respective presentation.

Both the written work, which deals with the contents of the curricular unit's program, as well as the respective presentation will take place in a phased manner throughout the semester.

Examinations or Special Assignments

Optional ndividual written work and respective phased presentation throughout the semester.

Special assessment (TE, DA, ...)

The exam score of 0-20 with a possible bonus up to a maximum of 2 values through optional written work and respective presentation through the semester.

Classification improvement

The exam score of 0-20 with a possible bonus up to a maximum of 2 values through optional written work and respective presentation through the semester.