OPTIMIZATION

The course aims at presenting the basic concepts and methods of optimization. The course provides students with the analytic tools to model and foresee situations in which a single decision-maker has to find the best choice. The course focuses on applications in economics, engineering, and computer science. At the end of the course, the students will be able to formulate mathematically real-life problems, solve them applying numerical methods, and realize what the optimal choice is.

The goals of the course are:

Knowledge and understanding: to acquire base knowledge that allows students to study optimization problems and apply opportune techniques to solve the decision-making problems. The students will be able to use algorithms for both linear and nonlinear programming problems.
Applying knowledge and understanding: 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.
Making judgments: to choose and solve autonomously complex decision-making problems and to interpret the solutions.
Communication skills: to acquire base communication and reading skills using technical language.
Learning skills: to provides 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.

For this course, there will be 2 hours of teaching per lecture twice a week. There will be both classroom lessons and laboratory lessons (if possible). 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.

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

1. LINEAR PROGRAMMING (12 hours)

Primal simplex method. Duality and dual simplex method.

2. IINTEGER PROGRAMMING (5 hours)

Branch and Bound method and cutting plane methods in integer programming; KP problem; TSP problem.

3. GAME THEORY (3 hours)

Nash equilibrium; zero-sum games; minimax solutions and linear programming.

4. NONLINEAR PROGRAMMING (4 hours)

Optimality conditions for nonlinear problems; numerical methods for constrained and not constrained problems.

5. SOFTWARE FOR OPTIMIZATION PROBLEMS (24 hours)

GeoGebra, Excel, AMPL, Mathematica.

1. F.S. Hillier, G.J. Lieberman, Introduction to Operations Research, Mc Graw Hill.
2. O.L. Mangasarian, Nonlinear Programming, SIAM Classics in Applied Mathematics.
3. D.P. Bertsekas, Convex Analysis and Optimization, Athena Scientific.
4. D.P. Bertsekas, Nonlinear Programming, Athena Scientific.

Other teaching material will be available on the platform Studium or MS Teams.