MATHEMATICAL METHODS FOR OPTIMIZATION

The course aims at presenting the basic concepts 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 attention focuses on applications in economics, engineering, and computer science. The students will be also able to solve numerically the problems using the AMPL code.

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 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 both classroom lessons and laboratory lessons (if possible).

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.

The course deals with linear and nonlinear optimization problems from both the theoretical and the
computational point of view. The following issues will be presented:

convex sets,
normal cones,
tangent cones,
optimality conditions,
duality,
algorithms for non linear problems,
multiobjective optimization,
AMPL implementations.

1. R. T. Rockafellar, R. J-B Wets, Variational Analysis

2. S. Boyd, L. Vandenberghe, Convex optimization

3. J. Jahn, Introduction to the Theory of Nonlinear Optimization - Springer- Verlag, Berlin (1996).

Other teaching material will be available on the platform Studium.