Optimization of Complex Systems - 60h
This course provides an understanding of advanced algorithms to tackle general optimization problems.
Instructor: Andrea Brilli
Term: Spring
Location: Mondays Room 48 Via Eudossiana, 18, Roma / Tuesdays Room A5, Via Ariosto, 25, Roma
Time: Mondays 14:00-16:00 / Tuesdays 15:00-18:00
Course Overview
The main goal of this course is to teach you how to design algorithms for different types of optimization problems. We’ll dig into both the practical and theoretical sides of:
- Derivative-Free methods
- Constraint-handling techniques
- Multiobjective problems
By the end, you should have the critical thinking skills to figure out when and why certain algorithmic approaches work better than others for a given problem.
Throughout the semester, we’ll also bring in guest seminars on various topics to keep things fresh and broaden your perspective.
Background material
- Multivariate Calculus: Italian notes English notes
- Basic concepts of Optimization Italian notes English notes
Reference Books
- “Derivative-Free and Blackbox Optimization” by C. Audet and W. Hare Link
- “Introduction to Derivative-Free Optimization” by A.R. Conn, K. Scheinberg, and L.N. Vicente Link
- “Multicriteria Optimization” by M. Ehrgott Link
- “Nonlinear Programming: Sequential Unconstrained Minimization Techniques” by A.V. Fiacco and G.P. McCormick Link
Exam
The exam consists of individual projects where you’ll implement optimization methods and explore theoretical topics. You’ll share your findings with the class through dedicated seminars. No exceptions, everyone presents.
About the seminars: the topics of the seminars are part of the program of the course, I will ask questions during the final seminars.
You can find the topics of the projects here. The projects can be done individually or you can make groups of maximum two people, the depth of the project will change accordingly. Starting from April 20th, there will be a weekly meeting for each student/group. The meeting are scheduled every Tuesday 13:00-14:00, and every Friday 10:30-13:00, in my office (A115, Via Ariosto). I will provide a template to fill in order to organize each week.
Schedule
| Week | Date | Topic | Materials |
|---|---|---|---|
| 1 | Feb 24 | Course Introduction Overview of mathematical optimization, course structure, and expectations. | |
| 1 | Feb 27 | Coordinate Search Basic derivative-free algorithmic structure with convergence analysis | |
| 2 | Mar 03 | Convergence Analysis Convergence Analysis of Coordinate descent and globalization strategies | |
| 2 | Mar 06 | Direct Search Direct Search and introduction to complexity analysis | |
| 3 | Mar 09 | Multiobjective Optimization Introduction to Multiobjective Optimization | |
| 3 | Mar 10 | Multiobjective Optimization Objective space structure, convex case, portfolio optimization, scalarization methods | |
| 4 | Mar 24 | Multiobjective Optimization Pareto Front approximation without scalarization | |
| 4 | Mar 27 | Multiobjective Optimization Quality of Pareto Front approximations | |
| 5 | Mar 31 | Inequality-constrained Optimization Introduction and Optimality Conditions | |
| 6 | Apr 13 | Inequality-constrained Optimization Proof of Fritz-John theorem and introduction to the logarithmic barrier | |
| 6 | Apr 14 | Inequality-constrained Optimization Sequential Interior methods. Theoretical proof and practical considerations | |
| 7 | Apr 20 | Optimization on Manifolds Seminar by Diego Scuppa | |
| 7 | Apr 21 | Optimization on Manifolds Seminar by Diego Scuppa | |
| 8 | Apr 27 | Proximal gradient methods Seminar by Elisa Trasatti | |
| 8 | Apr 28 | Proximal gradient methods Seminar by Elisa Trasatti |