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Optimization and Applications

Code: M3013     Acronym: M3013     Level: 300

Keywords
Classification Keyword
OFICIAL Mathematics

Instance: 2018/2019 - 1S Ícone do Moodle

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 1 Plano de estudos a partir de 2014 2 - 6 56 162
3
L:F 1 Official Study Plan 2 - 6 56 162
3
L:G 1 study plan from 2017/18 3 - 6 56 162
L:M 45 Official Study Plan 2 - 6 56 162
3
L:Q 0 study plan from 2016/17 3 - 6 56 162
Mais informaçõesLast updated on 2018-09-29.

Fields changed: Objectives, Fórmula de cálculo da classificação final, Palavras Chave, Componentes de Avaliação e Ocupação, Programa

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 and others.

  4. Acquire numeric skills in optimizing functions.

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

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

Jensen Paul A.; Operations research. ISBN: 0-471-38004-0
Press William H. 070; Numerical recipes. ISBN: 0-521-30811-9
Bakhvalov N. S.; Numerical methods

Complementary Bibliography

Stewart James; Cálculo. ISBN: 0-534-39-321-7

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 52,00
Total: 158,00

Eligibility for exams

Score greater than 9,5 points.

Calculation formula of final grade

Final classification = t1 + t2 + tc1 + tc2
t1 = 1st test score quoted to 8,5
t2 = 2st test score quoted to 8,5
tc1 = 1st computational work quoted to 1,5
tc1 = 2st computational work quoted to 1,5

NOTE: tc1 and tc2 are obtained during class time.

SECOND SEASON EXAM:
Final classification = er1 + er2 + tc1 + tc2
er1 = 1st exam score quoted to 8,5
er2 = 1st exam score quoted to 8,5
tc1, tc2 = tc1 and tc2 are 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).
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