Optimization and Applications
Keywords |
Classification |
Keyword |
OFICIAL |
Mathematics |
Instance: 2018/2019 - 1S 
Cycles of Study/Courses
Teaching language
Suitable for English-speaking students
Objectives
It is intended that students
- 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.
- Acquire skills in modeling and solving algorithmic real situations common in many scientific and economic activities.
- 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.
- 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).