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.
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.
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.
- 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;
- realizing the "matching" between the solving algorithm (to choose from existing or designing) and an appropriate processing software support.
Linear Algebra. Vector and matrix calculus. Basic concepts of Mathematical Analysis and Geometry.
Lectures and exercises
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
Lecture notes provided by the teacher and available in electronic format.
Ricevimento: By appointment.
September 17, 2018
Written.
Comprehension of the concepts explained during the Course.
Capability to:
- 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.
For the Laurea in Mathematics, which "borrows" only 7 cfu, the following topics are excluded:
