Studying at the University of Verona

Here you can find information on the organisational aspects of the Programme, lecture timetables, learning activities and useful contact details for your time at the University, from enrolment to graduation.

This information is intended exclusively for students already enrolled in this course.
If you are a new student interested in enrolling, you can find information about the course of study on the course page:

Laurea magistrale in Mathematics - Enrollment from 2025/2026

The Study Plan includes all modules, teaching and learning activities that each student will need to undertake during their time at the University.
Please select your Study Plan based on your enrollment year.

CURRICULUM TIPO:

1° Year 

ModulesCreditsTAFSSD
Insegnamenti offerti ad anni alterni
Insegnamenti offerti ad anni alterni
ModulesCreditsTAFSSD
Insegnamenti offerti ad anni alterni
Insegnamenti offerti ad anni alterni
Modules Credits TAF SSD
Between the years: 1°- 2°
Between the years: 1°- 2°
Ulteriori competenze
4
F
-

Legend | Type of training activity (TTA)

TAF (Type of Educational Activity) All courses and activities are classified into different types of educational activities, indicated by a letter.




S Placements in companies, public or private institutions and professional associations

Teaching code

4S00263

Credits

6

Language

Italian

Scientific Disciplinary Sector (SSD)

MAT/09 - OPERATIONS RESEARCH

Period

I semestre dal Oct 3, 2011 al Jan 31, 2012.

Learning outcomes

In this course we will provide an introduction to Convex Analysis in finite and infinite-dimensional spaces. We will show also some applications to problems of nonlinear optimizations and control theory arising from physics and economics.

Program

Review of weak topology on Banach spaces: convex sets, Minkowski functional, linear continuous operators, weak topology, separation of convex sets.

Convex functions: general properties, lower semicontinuous convex functions, convex conjugate, subdifferential in the sense of Convex Analysis. Introduction to Calculus of Variations.

Generalizations of convexity: differential calculus in Hilbert and Banach spaces, proximal and limiting subdifferential, the density theorem, sum rule, chain rule, generalized gradient in Banach space.

Introduction to control theory: multifunctions and trajectories of differential inclusions, viability,
equilibria, invariance, stabilization, reachability, Pontryagin Maximum Principle, necessary conditions
for optimality.

Application to optimization problems arising from physical or economic models.

Reference texts
Author Title Publishing house Year ISBN Notes
Ivar Ekeland and Roger Témam Convex Analysis and Variational Problems SIAM 1987 0-89871-450-8
F.H. Clarke, Y.S. Ledyaev, Ronald J. Stern, P.R. Wolenski Nonsmooth Analysis and Control Theory Springer-Verlag New York Inc. 1998 0387983368
Frank H. Clarke Optimization and Nonsmooth Analysis SIAM 1990 0-89871-256-4

Examination Methods

Written and oral examination. There will be also two partial tests during the course.

Students with disabilities or specific learning disorders (SLD), who intend to request the adaptation of the exam, must follow the instructions given HERE