. – Static and Dynamic Optimization
PROFF. MONICA BIANCHI, ANDREA CALOGERO, ENRICO MIGLIERINA
COURSE AIMS
The aim of the course is to provide the essential tools for the study of static and
dynamic optimization problems arising from economic applications.
COURSE CONTENT
The course will be divided into three parts.
First part (Monica Bianchi – 20 hours – first semester). Static Optimization for
real-valued functions.
Statement of a mathematical programming problem with some economical and
financial applications. Elements of convex analysis. Unconstrained optimization.
Optimization with equality and inequality constraints. Duality theory and convex
programming.
Second part (Enrico Miglierina – 20 hours – first semester). Multiobjective
Optimization.
Introduction to multiobjective optimization. Some examples. Partially ordered
vector spaces. Notions of solutions for a vector optimization problem.
Scalarization. Optimality conditions. Stability properties of the solutions.
Third part (Andrea Calogero – 32 hours – second semester). Dynamic
Optimization.
Some introductive problems. Statement of an optimal control problem. The
simplest problem of optimal control with variational approach. Singular controls
and bang-bang controls. More general problem of optimal control. Existence and
controllability problems. Optimal control with dynamic programming.
Relationships between variational method and dynamic programming.
READING LIST
O. GÜLER, Foundations of Optimization, Springer 2010
M. S. BAZARAA - H. D. SHERALI - C. M. SHETTY, Nonlinear Programming, John Wiley &
Sons, 1993
M. EHRGOTT, Multicriteria Optimization, Springer 2005
J. JAHN, Vector Optimization, Springer, 2011
A. CALOGERO, Notes on Optimal Control Theory, available on the web.
L.C. EVANS, An Introduction to Mathematical Optimal Control Theory, available on the
web.
TEACHING METHOD
Lectures.
ASSESSMENT METHOD
Written exam with both practical and theoretical questions. Two partial tests are planned
at the end of each semester.
NOTES
Announcements, detailed program and additional materials will be provided on
Blackboard.
Office hours: appointment by mail:
Monica Bianchi: monica.bianchi@unicatt.it
Andrea Calogero: andrea.calogero@unimib.it
Enrico Miglierina: enrico.miglierina@unicatt.it