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
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.
1° Year
Modules | Credits | TAF | SSD |
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One course chosen from the following
One course chosen from the following
2° Year activated in the A.Y. 2013/2014
Modules | Credits | TAF | SSD |
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Modules | Credits | TAF | SSD |
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One course chosen from the following
One course chosen from the following
Modules | Credits | TAF | SSD |
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Modules | Credits | TAF | SSD |
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One course chosen from the following
One course chosen from those that will be activated from the following
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 (2013/2014)
Teaching code
4S001106
Teacher
Coordinator
Credits
6
Language
English
Scientific Disciplinary Sector (SSD)
MAT/05 - MATHEMATICAL ANALYSIS
Period
I semestre dal Oct 1, 2013 al Jan 31, 2014.
Location
VERONA
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 |
---|---|---|---|---|---|
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.