# MATHEMATICAL METHODS FOR OPTIMIZATION

Academic Year 2021/2022 - 1° Year
Teaching Staff: Laura Rosa Maria SCRIMALI
Credit Value: 6
Scientific field: MAT/09 - Operational research
Taught classes: 35 hours
Exercise: 12 hours
Term / Semester:

## Learning Objectives

The course aims at presenting well-known optimization methods. The course provides students with the analytic tools to model and solve numerically 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 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.

## Course Structure

For this course, there will be 2 hours of teaching per lecture twice a week. During the classroom lessons a graphics tablet will be used. The hand-written slides will be available on the platform Studium. 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.

## Detailed Course Content

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 for differentiable and non differentiable optimization,
duality,
algorithms for non linear problems (gradient, Newton, penalty method, augmented Lagrangian),
multiobjective optimization.

## Textbook Information

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.