The course will introduce the basic mathematical concepts necessary to construct algorithms for the solution of optimization problems. The main focus will be on "easy" (constrained or unconstrained, convex, continuous) optimization problems, and their (local) solution algorithms, relevant for applications in Data Science / Machine Learning / Artificial Intelligence, among others, with a view on providing to the students solid methodological foundations useful for the several subsequent courses in these areas. However, the course will also cover some material related to "hard" (mixed-integer, nonconvex) optimization problems, and their (global) solution algorithms, with a view of providing the students with the concept of Prescriptive Analytics as "the final step" of Data Science, and therefore a motivation for the more advanced courses related to optimization.

The course has two distinct tracks for evaluating knowledge: written + oral exam or didactic project + oral exam.

For the first track, the student will be assessed on her/his demonstrated ability to answer questions regarding small-scale optimization problems, which may involve the application of the solution algorithms studied in the course. The ability of developing mathematical models for some (small, simplified) applications will also be tested. During the oral exam the student must be able to demonstrate her/his knowledge of the theory underlying the models and the algorithms sudied during the course together with adequate language and proper terminology. Critical awareness of the topics will be also evaluated.

For the second track, the student will be assessed on her/his demonstrated ability to apply the main course contents to one specific problem, developing an end-to-end application to solve it and a report that describes the application and analyzes critically its perfoirmances.  During the oral exam the student must be able to demonstrate her/his knowledge of the course material together with adequate language and proper terminology. Critical awareness of the topics will be also evaluated.

The student will acquire some knowledge of the theoretical properties of some basic problems in optimization and on the functioning of the corresponding solution algorithsm. The student will therefore be able to identify the class to which a given optimization problem belongs, together with the best available solution method (among those studied, and possibly beyond) to solve them, to  correlate the known theoretical properties with the practical behavior of the approaches in order to both check their correctness and possibly improve their efficiency/effectiveness. The student will also be able to autonomously propose mathematical (optimization) models for some simple applications. Finally, students choosing the didactic project evaluation track will learn to develop, debug, test, improve and use software to solve optimization problems.

The assessment will be based onthe results of either the written exam or the didactic project, deoending on the track freely chosen by each student, and of the oral exam.

The student will learn to combine analysis and computer implementations to solve the main problems underlying Data Science, as well as using Data Science approaches to develop and solve models of (simplified) application programs. This will require critical assessment of the properties of the problem at hand, analysys of the alternative solution approaches, and possibly creativity for proposing models and algorithms. The students choosing the didactic project + oral exam track will have to learn teamwork strategies, since the projects are supposed to be developed in pairs, as well as proper interaction with the committents of a complex project (the lecturer), both vis-a-vis and via e-mail or other electronic means.

The behaviors will be continuously assessed during the course, the written exam or the development of the project, and the final oral exam.