## OPTIMIZATION METHODS OPTIMIZATION METHODS

A.Y. Credits
2021/2022 4
Lecturer Email Office hours for students
Raffaella Servadei Monday and Tuesday 11-12 a.m. or by appointment
Teaching in foreign languages
Course entirely taught in a foreign language English
This course is entirely taught in a foreign language and the final exam can be taken in the foreign language.

### Assigned to the Degree Course

Research Methods in Science and Technology (XXXVII)
Curriculum: PERCORSO COMUNE
Date Time Classroom / Location
Date Time Classroom / Location

### Learning Objectives

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

### Program

01. Introduction to optimization.

02. Optimization:

02.01  Local and global maxima and minima for functions.

02.02  Critical points for functions.

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

### Bridging Courses

There are no mandatory prerequisites.

### Learning Achievements (Dublin Descriptors)

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.

### Teaching Material

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

### Didactics, Attendance, Course Books and Assessment

Didactics

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.

### Additional Information for Non-Attending Students

Didactics

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.

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