OVERVIEW

The Course introduces to optimization models and methods for the solution of decision problems. It is structured according to the basic topics of problem modelling, its tractability, and its solution by means of algorithms that can be implemented on computers.  Case studies from Information Technology are presented and investigated.

AIMS AND CONTENT

LEARNING OUTCOMES

The Course introduces optimization models and methods that can be used to solve decision-making problems. It is part of the fundamental themes of problem modeling, study of computational handling, and resolution through algorithms that can be implemented on a computer. Various application contexts are considered, and some "case studies" in the IT field are discussed in detail. The aim of the course is to acquire the skills to deal with application problems by developing models and methods that work efficiently in the presence of limited resources. Students will be taught to: interpret and shape a decision-making process in terms of an optimization problem, identifying decision-making variables, the cost function to minimize (or the merit digit to maximize) and constraints; Framing the problem in the range of problems considered "canonical" (linear / nonlinear, discrete / continuous, deterministic / stochastic, static / dynamic, etc.); Realizing the "matching" between the solving algorithm (to choose from existing or designing) and an appropriate processing software support.

AIMS AND LEARNING OUTCOMES

The students will be taught to:

- interpret and shape a decision-making process in terms of an optimization problem, identifying the decision-making variables, the cost function to minimize (or the figure of merit to maximize), and the constraints;

- framing the problem in the range of problems considered "canonical" (linear / nonlinear, discrete / continuous, deterministic / stochastic, static / dynamic, etc.);

- realizing the "matching" between the solving algorithm (to choose from existing or to be designed) and an appropriate processing software support.

The students will be taught to:

- interpret and shape a decision-making process in terms of an optimization problem, identifying decision-making variables, the cost function to minimize (or the merit digit to maximize) and constraints;

- framing the problem in the range of problems considered "canonical" (linear / nonlinear, discrete / continuous, deterministic / stochastic, static / dynamic, etc.);

- realizing the "matching" between the solving algorithm (to choose from existing or designing) and an appropriate processing software support.

PREREQUISITES

Linear Algebra. Vector and matrix calculus. Basic concepts of Mathematical Analysis and Geometry.

TEACHING METHODS

Lectures and exercises

SYLLABUS/CONTENT

INTRODUCTION TO OPERATIONS RESEARCH

LINEAR PROGRAMMING

DUALITY

INTEGER PROGRAMMING

GRAPH AND NETWORK OPTIMIZATION

COMPLEXITY THEORY

NONLINEAR PROGRAMMING

DYNAMIC PROGRAMMING

CASE STUDIES FROM INFORMATION TECHNOLOGY

SOFTWARE TOOLS FOR OPTIMIZATION

RECOMMENDED READING/BIBLIOGRAPHY

Lecture notes provided by the teacher and available in electronic format.

TEACHERS AND EXAM BOARD

LESSONS

LESSONS START

September 17, 2018

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

Written.

ASSESSMENT METHODS

Comprehension of the concepts explained during the Course.

Capability to:

- interpret and shape a decision-making process in terms of an optimization problem, identifying the decision-making variables, the cost function to minimize (or the figure of merit to maximize), and the constraints;

- frame the problem in the range of problems considered "canonical" (linear / nonlinear, discrete / continuous, deterministic / stochastic, static / dynamic, etc.);

- choose and/or develop a solving algorithm and apply it to solve the problem.

Exam schedule

FURTHER INFORMATION

For the Laurea in Mathematics, which "borrows" only 7 cfu, the following topics are excluded:

DYNAMIC PROGRAMMING

CASE STUDIES FROM INFORMATION TECHNOLOGY