Optimization (2011/2012)

Course code
Name of lecturer
Antonio Marigonda
Antonio Marigonda
Number of ECTS credits allocated
Academic sector
Language of instruction
I semestre dal Oct 3, 2011 al Jan 31, 2012.

Lesson timetable

I semestre
Day Time Type Place Note
Tuesday 3:30 PM - 5:30 PM lesson Lecture Hall M from Oct 18, 2011  to Jan 31, 2012
Friday 3:30 PM - 5:30 PM lesson Lecture Hall M from Oct 21, 2011  to 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.


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 books
Author Title Publisher Year ISBN Note
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

Assessment methods and criteria

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

Statistics about transparency requirements (Attuazione Art. 2 del D.M. 31/10/2007, n. 544)

Outcomes Exams Outcomes Percentages Average Standard Deviation
Positive 75.0% 25 1
Rejected 12.5%
Absent 12.5%
Ritirati --
Canceled --
Distribuzione degli esiti positivi
18 19 20 21 22 23 24 25 26 27 28 29 30 30 e Lode
0.0% 0.0% 0.0% 16.6% 0.0% 0.0% 0.0% 16.6% 66.6% 0.0% 0.0% 0.0% 0.0% 0.0%

Data from AA 2011/2012 based on 8 students. I valori in percentuale sono arrotondati al numero intero più vicino.