OPTIMIZATION

The course introduces the main methods of mathematical optimization, providing the theoretical and computational tools needed to model and solve decision-making problems. By the end of the course, students will be able to formulate mathematical models, apply appropriate solution methods, and interpret the results.

The goals of the course are:

To acquire base knowledge that allows students to study optimization problems and apply opportune techniques to solve decision-making problems. The students will be able to use algorithms for both linear and nonlinear programming problems.
To identify and model real-life decision-making problems. In addition, through real examples, the student will be able to find correct solutions for complex problems.
To choose and solve autonomously complex decision-making problems and to interpret the solutions.
To acquire base communication and reading skills using technical language.
To provide students with theoretical and practical methodologies and skills to deal with optimization problems, ranging from computer science to engineering. To acquire further knowledge on the problems related to applied mathematics.

Teaching Organization

credit value 6 - 48 hours

total study 150 hours

102 hours of individual study

24 hours of frontal lecture

24 hours of exercises

 

For this course, there will be 2 hours of teaching per lecture twice a week. The teaching material will be available on the Studium and Teams platforms. 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.

Fundamental concepts of mathematical analysis, two-dimensional geometry and linear algebra.

For a thorough understanding of the topics covered and the methodologies presented, regular attendance at the lectures is strongly recommended.

The course aims to study the theoretical foundations and main solution methodologies of mathematical optimization. The objective of the course is to enable students to translate complex problems into a mathematical formulation in terms of linear or nonlinear programming and to solve them using appropriate numerical methods. By the end of the course, students will be able to construct a mathematical model of a real decision-making problem and interpret the obtained solution as an operational strategy. Particular emphasis will be placed on applications in the socio-economic, computer science, and engineering fields.

Goals of U. N. Agenda for Sustainable Development

This course contributes to the achievement of the following goals of U. N. Agenda for Sustainable Development

 

Goal N. 4 Quality Education

      Target 4.3

     Target 4.7

        

 

Goal N. 13  Climate Action

        Target  13.3

[1]   F.S. Hillier, G.J. Lieberman, Introduction to Operations Research, Mc Graw Hill, 2020

[2]  O.L. Mangasarian, Nonlinear Programming, SIAM Classics in Applied Mathematics.
[4]   D.P. Bertsekas, Nonlinear Programming, Athena Scientific.

Teaching material will be given during the course.

The final exam consists of an oral test during which the candidate is also requested to solve a numerical exercise. The final grade is established on the basis of the answers given by the candidate and the solving of the numerical example.
Final grades will be assigned taking into account the following criteria:
Rejected: Basic knowledge has not been acquired. The student is not able to solve simple exercises.
18-23: Basic knowledge has been acquired. The student solves simple exercises, has sufficient communication skills, and makes judgements.
24-27: All the knowledge has been acquired. The student solves all the proposed exercises making few errors and has good communication skills and making judgements.
28-30 cum laude: All the knowledge has been completely acquired. The student applies knowledge and has excellent communication skills, learning skills and making judgements.
 
Learning assessment may also be carried out on-line, should the conditions require it.

To ensure equal opportunities and in compliance with current laws, interested students may request a personal interview in order to plan any compensatory and/or dispensatory measures based on educational objectives and specific needs. Students can also contact the CInAP (Centro per l’integrazione Attiva e Partecipata — Servizi per le Disabilità e/o i DSA) referring teacher within DMI (https://web.dmi.unict.it/it/corsi/lm-18/referente-cinap).

To take part in the final exam, students must register through the SmartEdu portal. For any technical issues related to the registration, please contact the Student Office.

Simplex method.  Linear programming examples. Integer linear programming and use of branch and bound method. Knapsack problem. Optimality conditions in linear programming. Optimality conditions for non linear problems. KKT conditions. Penalty and barrier methods.
It should be noted that these questions are purely indicative: the actual questions asked during the exam may differ, even significantly, from those included in this list.
During the lessons, exercises similar to those that students will face in their final exam will be carried out. Additional exercises will be made available throughout the course.