Ph.D. Course

Distributed algorithms for optimization and control over networks

Ph.D. in Information Technology

Dipartimento di Elettronica, Informazione e Bioingegneria (DEIB)

Politecnico di Milano


Dates: February 10 - 11, 2020

Location: DEIB, Building n. 20, Politecnico di Milano


Dates: April 15 - 17, 2020

Location: online lectures



Maria Prandini - Politecnico di Milano



Alessandro Falsone - Politecnico di Milano

Simone Garatti - Politecnico di Milano

Kostas Margellos - Oxford University

Maria Prandini - Politecnico di Milano


Course description:

This course will introduce the students to a mathematical framework for the analysis and design of distributed decision-making schemes in multi-agent systems seeking convergence to the optimal cooperative solution. The case when uncertainty is affecting the multi-agent system is also addressed.

The course is structured in 4 parts.

1. Motivation and illustrative applications

Introduction to decision making problems arising in smart grid control and optimization, and in coordination and control for electric vehicle fleets.

2. Mathematical tools

Introduction to the mathematical tools of graph theory, convex analysis, optimization, duality theory that constitute the theoretical backbone for the analysis and design of cooperative algorithms

3. Distributed cooperative algorithms

Primal-based and dual-based algorithms for distributed cooperative decision making will be illustrated, resting on the math tools of Part 2

4. Distributed optimization in uncertain networks

The algorithmic solutions described in Part 3 will be extended to the case when the multi-agent optimization problem is affected by uncertainty.


Lectures will take place at Building n. 20 of the Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, via Ponzio 34/5, 20133 Milano.

See for directions on how to reach the Dipartimento di Elettronica, Informazione e Bioingegneria.


Structure of the course:

Monday, February 10 - Room Sala seminari Nicola Schiavoni

11:30 - 13:00 Motivation [file pdf] and graph theory [file pdf]
14:30 - 17:00 Math tools [file pdf]

Tuesday, February 11 - Room Sala seminari Nicola Schiavoni

09:30 - 11:00 Math tools [file pdf]

14:30 - 17:00 Math tools [file pdf]

Wednesday, April 15 - Online lectures

11:30 - 13:00 Primal-based algo

14:30 - 17:00 Primal-based algo

Thursday, April 16 - Online lectures

09:30 - 12:00 Duality-based algo
14:30 - 16:00 Duality-based algo

Friday, April 17 - Online lectures

09:30 - 12:00 Distributed uncertain optimization

14:30 - 16:00 Distributed uncertain optimization



The above time schedule does not include breaks but refers to effective lecture-time.

 The slides of the course will be posted in due course on this website.


Relevant references:

D. Bertsekas, J.N. TsitsiklisParallel and distributed computation: Numerical methods, Editore: Athena Scientific

K. Margellos, A. Falsone, S. Garatti, M. Prandini. Distributed Constrained Optimization and Consensus in Uncertain Networks via Proximal Minimization. IEEE Transactions on Automatic Control, 2018

A. Falsone, K. Margellos, S. Garatti, M. Prandini.Dual decomposition for multi-agent distributed optimization with coupling constraints. Automatica, 2017

Additional references will be provided in the slides of the lectures.