Optimization (2013/2014)

Course code
4S001106
Name of lecturer
Antonio Marigonda
Coordinator
Antonio Marigonda
Number of ECTS credits allocated
6
Academic sector
MAT/05 - MATHEMATICAL ANALYSIS
Language of instruction
English
Period
I semestre dal Oct 1, 2013 al Jan 31, 2014.

Lesson timetable

I semestre
Day Time Type Place Note
Wednesday 1:30 PM - 3:30 PM lesson Lecture Hall M  
Friday 1:30 PM - 3:30 PM lesson Lecture Hall M  

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.

Syllabus

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)

Data from AA 2013/2014 are not available yet