The student is expected to acquire knowledge of the main numerical methods for solving large-scale numerical optimization problems, according to the problem type, to develop the ability to choose and correctly apply software for different numerical optimization problems, and to perform a critical investigation of the results obtained.

Knowledge of basic linear algebra and calculus, as well as a basic coding ability.

Unconstrained optimization: - gradient and conjugate gradient methods for linear systems - descent methods - Newton, quasi-Newton, and modified Newton methods - Gauss-Newton method - line-search strategies Constrained optimization: - Optimality conditions - Projected gradient method - Penalty methods - Alternating direction method of multipliers (ADMM) Stochastic optimization: - Static simulation-based optimization (parametric optimization) - Dynamic simulation-based optimization (control optimization)

The course is organized into theoretical lectures and practice classes. Theoretical lectures are devoted to the presentation of the topics, with definitions, properties, and introductory examples. The practice classes are devoted to training the students’ abilities to solve problems and exercises and to perform computations and simulations with common tools.

Slides presented during lesson will be made avalaible through the Portale della Didattica. Other material will be suggested in class and, if possible, made avalaible through the Portale della Didattica. Suggested textbook: J. Nocedal, S. J. Wright, Numerical Optimization, Springer, 2006 A. Gosavi, Simulation-Based Optimization, 2nd edition, Springer, 2015

Lecture slides; Text book; Exercise with solutions ; Lab exercises with solutions; Video lectures (previous years);

You can take this exam before attending the course

Exam: Compulsory oral exam; Group essay;

The exam is based on homework reports assigned during the course and on an oral discussion. In detail, some problems will be assigned during the semester, aimed at testing students' ability to identify the correct strategy to solve the problem, apply the methods presented during the lectures, and comment on the practical behavior of the methods applied on some given test cases. The students have to choose two assignments among the proposed ones and write a report for each assignment. Assignment 1 has to be chosen among the stochastic optimization proposals; Assignment 2 has to be chosen among the unconstrained/constrained optimization proposals. The report should be the result of teamwork, with each team made of 2 or 3 students. The oral discussion will be then organized as follows: a1) a discussion on Assignment 1, aimed at testing the depth of the student's understanding of the subjects and their ability to explain, defend, reflect, critically evaluate, and possibly improve their work; a2) a discussion on Assignment 2, aimed at testing the depth of the student's understanding of the subjects and their ability to explain, defend, reflect, critically evaluate, and possibly improve their work; a3) a discussion on other topics studied in the course, with a special focus on (but not limited to) topics not addressed by the report. Both theoretical aspects and implementation issues and examples of fields of applications will be discussed. The grading of parts a1) and a2) will be based both on the quality of the reports and on their oral defense. The maximum grading attainable is: - 8 points for part (a1) - 12 points for part (a2) - 12 points for part (a3) The final course grade is obtained by summing up the grades obtained for each part (a1)-(a3).

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.