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.
Study Plan
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 2025/2026The 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.
1° Year
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2° Year activated in the A.Y. 2011/2012
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Due tra i seguenti insegnamenti
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Due tra i seguenti insegnamenti
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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.
Optimization (2011/2012)
Teaching code
4S00263
Teacher
Coordinator
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.
Author | Title | Publishing house | Year | ISBN | Notes |
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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.