PERIODO: APRILE - MAY 2015

The aim of the course is to strengthen the knowledge of optimization methods, extending modeling and
solution procedures to cases affected by significant uncertainty. Uncertainty is pervasive in many
branches of engineering and social sciences, including finance, supply chain management, energy
markets, and telecommunication networks. Emphasis is on stochastic programming models, but, since a
stochastic characterization of uncertainty is not always available, reliable, or appropriate, we will also
consider robust optimization frameworks. Furthermore, since solving multistage stochastic optimization
models is quite challenging, we will also deal with approximate dynamic programming methods that,
among other things, illustrate the connection between mathematical optimization and machine learning.
Case studies and examples are used throughout the course to illustrate the relevance of its content.
Prerequisites: Some familiarity with standard linear programming models; essentials of probability
theory.
CONTENT
· Introductory examples and motivations; the impact of uncertainty; expected value of perfect
information and value of the stochastic solution.
· Alternative paradigms: stochastic programming with recourse; chance-constrained optimization;
robust optimization.
· A refresher on optimization theory: convexity; duality; solution methods for linear, nonlinear, and
mixed-integer programming models.
· Decomposition methods for stochastic programming models with recourse.
· Solution methods for mixed-integer stochastic optimization models.
· The formulation of dynamic optimization models under uncertainty.
· Scenario generation: Monte Carlo sampling; deterministic methods (quasi-Monte Carlo, Gaussian
quadrature, moment matching).
· Risk measurement and management: utility functions; coherent risk measures.
· Simulation-based optimization.
· Dynamic programming: Bellman's equation; learning the value function by Monte Carlo simulation
and linear regression.
· Robust optimization: nonstochastic representation of uncertainty; solution methods based on
convex optimization.

The aim of the course is to strengthen the knowledge of optimization methods, extending modeling and solution procedures to cases affected by significant uncertainty. Uncertainty is pervasive in many branches of engineering and social sciences, including finance, supply chain management, energy markets, and telecommunication networks. Emphasis is on stochastic programming models, but, since a stochastic characterization of uncertainty is not always available, reliable, or appropriate, we will also consider robust optimization frameworks. Furthermore, since solving multistage stochastic optimization models is quite challenging, we will also deal with Approximate Dynamic Programming methods that, among other things, illustrate the connection between mathematical optimization and machine learning. Case studies and examples are used throughout the course to illustrate the relevance of its content.
Prerequisites: some familiarity with standard linear programming models; essentials of probability theory.

ASSESSMENT
Please note that, unlike previous editions of the course, in order to formally record the associated credits
(6), passing a written exam is required. We will arrange two dates, one before and one after summer. The
exam is closed book, but not quite challenging, as its aim is just to provide PhD students with some
incentive to actively follow the course and get acquainted with its content.
SCHEDULE
Lectures will be given at Dipartimento di Scienze Matematiche (DISMA), Politecnico di Torino, in Aula
Buzano (the internal lecture/seminar room of DISMA, third floor).
Lecture Date Time
1 Friday, April 10th 9:30 - 12:30
2 Monday, April 13th 9:30 - 12:30
3 Tuesday, April 21st 9:30 - 12:30
4 Monday, April 27th 9:30 - 12:30
5 Monday, May 4th 9:30 - 12:30
6 Monday, May 11th 9:30 - 12:30
7 Monday, May 18th 9:30 - 12:30
8 Friday, May 22nd 9:30 - 12:30
9 Monday, May 25th 9:30 - 12:30
10 Friday, May 29th 9:30 - 12:30