OPTIMIZATION

MAT/09 - 6 CFU - 1° semestre

Docente titolare dell'insegnamento

PATRIZIA DANIELE


Obiettivi formativi

This graduated-level course introduces analytic tools and optimization methods that are suitable for large-scale problems arising in data science applications. The course presents both basic and advanced concepts of optimization and explores several algorithms that are efficient for networks problems.

The student will acquire the ability to formulate, in mathematical terms, problems related to profit maximization and cost minimization, optimization of resources, and traffic network equilibria.
The goals of the course are:

Knowledge and understanding: the aim of the course is to acquire advanced knowledge that allows students to study optimization problems and model techniques of large-scale decision-making problems. The students will be able to use algorithms for both linear and nonlinear programming problems.
Applying knowledge and understanding: students will acquire knowledge useful to identify and model real-life decision-making problems. In addition, through real examples, the student will be able to implement correct solutions for complex problems.
Making judgments: students will be able to choose and solve autonomously complex decision-making problems and to interpret the solutions.
Communication skills: students will acquire base communication and reading skills using technical language.
Learning skills: the course provides students with theoretical and practical methodologies and skills in to deal with large-scale optimization problems.


Modalità di svolgimento dell'insegnamento

There will be both classroom lessons and laboratory lessons. For each topic, exercises will be solved by the teacher or proposed to students.

Should teaching be carried out in mixed mode or remotely, it may be necessary to introduce changes with respect to previous statements, in line with the programme planned and outlined in the syllabus.


Prerequisiti richiesti

Basic elements of vectors and matrices, vector spaces, linear equations, inequalities.



Frequenza lezioni

Attendance is strongly recommended.



Contenuti del corso

Linear Programming (LP) (about 13 h)
LP models; Graphical method; Simplex method; Duality; Sensitivity analysis

Integer Linear Programming (ILP) (about 9 h)
Branch & Bound method; 0-1 programming; Knapsack problem

Software (about 5 hours)

Excel, Mathematica, Wolfram Code, Lingo

Network problems (about 13 h)

Graphs (Kruskal, Dijkstra, Bellman-Kalaba algorithms)



Testi di riferimento

  1. J. Stacho, Introduction to Operations Research, Columbia University, NY, http://www.cs.toronto.edu/~stacho/public/IEOR4004-notes1.pdf
  2. M.S. Bazaraa, J.J. Jarvis, H.D. Sherali, Linear Programming and Network Flows, John Wiley & Sons, 2009.
  3. F. Hillier, G.J. Liebermann, “Introduction to Operations Research”, McGraw-Hill, 2006

Altro materiale didattico

  1. R. Tadei, F. Della Croce, A. Grosso, “Fondamenti di Ottimizzazione”, Società Editrice Esculapio, 2005;
  2. R. Baldacci, M. Dell’Amico, “Fondamenti di Ricerca Operativa”, Pitagora Editrice, 2002;
  3. M. Bruglieri, A. Colorni, “Ricerca Operativa”, Zanichelli, 2012;
  4. M. Caramia, S. Giordani, F. Guerriero, R. Musmanno, D. Pacciarelli, “Ricerca Operativa”, Isedi, 2014
  5. F. Fumero, Metodi di ottimizzazione. Esercizi ed applicazioni, Società Editrice Esculapio, 2013
  6. L. Grippo, M. Sciandrone, Metodi di Ottimizzazione Non Vincolata, Springer, Unitext 2011.
  7. R. Tadei, F. Della Croce, “Elementi di Ricerca Operativa”, Società Editrice Esculapio, 2005;
  8. M.S. Bazaraa, J.J. Jarvis, H.D. Sherali, Linear Programming and Network Flows, John Wiley & Sons Inc., 2009
  9. S. Boyd, L. Vandenberghe, Convex optimization, https://web.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf

Dispense su STUDIUM http://studium.unict.it



Programmazione del corso

 ArgomentiRiferimenti testi
1Simplex Method1, 2 
2Duality in LP1, 2 
3Sensitivity Analysis
4Branch & Bound method
5The Knapsak problem1, 2 
6Graph Algorithms


Verifica dell'apprendimento


MODALITÀ DI VERIFICA DELL'APPRENDIMENTO

The final exam consists of an oral test during which the candidate shows that he has assimilated the topics covered in the course.

Learning assessment may also be carried out on line, should the conditions require it.


ESEMPI DI DOMANDE E/O ESERCIZI FREQUENTI

The symplex method.

The strong duality theorem.

The Branch & Bound algorithm.

The knapsack problem.

The shortest path algorithm.




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