Aim of the course is to give to the students some basic tools and topics in optimization methods.

01. Introduction to optimization.

02. Optimization:

02.01  Local and global maxima and minima for functions.

02.02  Critical points for functions.

02.03  Gradient method.

02.04  Necessary and sufficient conditions for local maxima and minima.

02.05  Classification of critical points.

03. Minimization techniques:

03.01  Weierstrass theorem.

03.02  Direct methods of the Calculus of Variations.

03.03  Critical point theory.

03.04  Minimax methods.

04. Applications of optimization

There are no mandatory prerequisites.

Knowledge and understanding: at the end of the course the student will learn the basic notions of mathematical optimization.

Applying knowledge and understanding: at the end of the course the student will learn the methodologies of mathematical optimization and will be able to apply them to the study of various problems.

Making judgements: at the end of the course the student will be able to apply the techniques of mathematical optimization in order to solve new problems, also coming from real-world applications.

Communications skills: at the end of the course the student will have the ability to express the fundamental notions of mathematical optimization using a rigorous terminology.

Learning skills: during the course the student will learn the ability to study the notions of mathematical optimization, also in order to use it in solving different kind of problems.

The teaching material prepared by the lecturer in addition to recommended textbooks (such as for instance slides, lecture notes, exercises, bibliography) and communications from the lecturer specific to the course can be found inside the Moodle platform › blended.uniurb.it

Teaching

Theorical and practical lessons.

Attendance

Although strongly recommended, course attendance is not mandatory.

Course books

Adams R.A. – Essex C., Calculus: a complete course, Pearson Education Canada, 2013.

Badiale M. - Serra E., Semilinear Elliptic Equations for Beginners, Springer-Verlag, London, 2011.

Rabinowitz P.H., Minimax methods in critical point theory with applications to differential equations, CBMS Reg. Conf. Ser. Math., 65, American Mathematical Society,  Providence, RI (1986).

Struwe M., Variational Methods, Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems, Ergebnisse der Mathematik und ihrer Grenzgebiete, \textbf{3}, Springer Verlag, Berlin-Heidelberg, 1990.

 Willem M., Minimax Theorems, Progress in Nonlinear Differential Equations and their Applications, 24, Birkhauser, Boston, 1996.

Assessment

The exam of Optimization Methods consists of a written exam on the topics of the course.  

Disability and Specific Learning Disorders (SLD)

Students who have registered their disability certification or SLD certification with the Inclusion and Right to Study Office can request to use conceptual maps (for keywords) during exams.

To this end, it is necessary to send the maps, two weeks before the exam date, to the course instructor, who will verify their compliance with the university guidelines and may request modifications.

Teaching

As for attending students.

Attendance

As for attending students.

Course books

As for attending students.

Assessment

As for attending students.

Disability and Specific Learning Disorders (SLD)

Students who have registered their disability certification or SLD certification with the Inclusion and Right to Study Office can request to use conceptual maps (for keywords) during exams.

To this end, it is necessary to send the maps, two weeks before the exam date, to the course instructor, who will verify their compliance with the university guidelines and may request modifications.