Corso di laurea in Informatica

Students must learn basic notions of geometry and the essential techniques for manipulating vectors and matrices in n-dimensional spaces, and become capable of formulating and solving simple linear programs.

KNOWLEDGE AND UNDERSTANDING Acquisition of knowledge about principles and techniques of linear programming, knowledge of the basic mechanisms of algorithms that operate on such models, and the related theory.

APPLYING KNOWLEDGE AND UNDERSTANDING Acquisition of basic concepts in algebra and geometry concepts, and the ability of formulating linear programming models ---- both with continuous variables and integer variables ---- starting from the statement of a real problem.

MAKING JUDGMENTS Acquisition aware judgment concerning the types of models suitable for representing a real problem and in selecting suitable solution approaches on the basis of the available computational resources.

COMMUNICATION SKILLS Acquisition of skills and tools suitable to actively discuss the modeling issues and the algorithmic aspects of common optimization problems, and the mathematics underlying the most common algorithms for linear programming.

LEARNING SKILLS Acquisition of autonomous learning skills in modeling and algorithmic fields.

Validity of results and scores:

• The mark obtained by a student in an exam will be held valid throughout the whole current academic year.
• Repetition of the exam, even if the student withdraws from the session, fully invalidates any previous mark.

1. Vectors and matrices. Basic operations. Convex sets and polyhedra.
2. Solutions of a system of linear equations.
3. Linear combinations, linear independence.
4. Linear programming.
   • Modeling.
   • Structure of the feasible region. Graphical solution for linear programs.
   • Basic feasible solutions. The simplex algorithm for linear programs.