Optimisation
Download in PDF- Lecturer: OSSART Florence (florence.ossart@sorbonne-universite.fr)
- Course code: UM4RBT10-Opt
- Student workload: 8h of lectures, 6h of tutorials, 10h of labs
- Credits: 3 ECTS
- Specialization tracks:
- Semester offered: S1 S2 S3 S4
- Language of instruction: French English
- Targeted audience: Eng. Sc. department Other :
- Localization : PMC Campus Other :
Course Overview
This course aims to teach students how to define and numerically solve a simple continuous optimization problem, with or without constraints.
Mots-clés :
Prerequisites
Students should have previously acquired the following prerequisites to follow this course:
- Mathematics: Systems of linear equations and matrices, functions of several variables
- Programming: Python basics, classical algorithms
Intended Learning Outcomes
By the end of this course, students will be able to:
- Formulate a simple continuous optimization problem (decision variables, objective function, constraints), choose and implement a solution method and perform a critical analysis of the results
- Know the theoretical bases of the main methods of continuous optimization without constraints (gradient descent, Newton)
- Know the theoretical bases of the main methods of continuous optimization under constraint-equality (Lagrange multipliers)
- Know the theoretical bases of the main methods of continuous optimization under constraint-inequality (KKT algorithm)
- Understand what a multi-objective optimization problem is and the concept of dominance
- Know the principle of some heuristic optimization methods (Monte-Carlo, genetic algorithms, SPO, ...)
- Implement and code in python the solution of a simple optimization problem, analyze the behavior of the method according to the hyperparameters of the method used
Indicative Teaching Sequence and Methods
| Week | C/TD/TP* | Content | Preparation | Learn.\ outc. |
|---|---|---|---|---|
| S1 | C1 (2h), TD1 (2h) | Unconstrained continuous minimization, analytical approach | Personal work in addition: visualization in python of the solutions of the tutorial exercises | AAV1, AAV2 |
| S2 | TP1 (4h) | Unconstrained continuous minimization, numerical approach (gradient descent) | AAV1, AAV2, AAV7 | |
| S3 | C2 (2h), TD2 (2h) | Continuous minimization under equal constraints | Personal work in addition: visualization in python of the solutions of the tutorial exercises | AAV1, AAV3 |
| S4 | TP2 (4h) | Continuous minimization under equal constraints | AAV1, AAV3, AAV7 | |
| S5 | C3 (2h), TD3 (2h) | Continuous minimization under constraints-inequalities - Multi-objective optimization | Personal work in addition: visualization in python of the solutions of the tutorial exercises | AAV1, AAV4, AAV6, AAV7 |
| S6 | C4 (2h), TP3 (2h) | Multi-objective optimization - Some heuristic methods of optimization | AAV1, AAV5, AAV6, AAV7 | |
| S7 | TP4 (2h) | Examination | AAV7 |
- C/TD/TP respectively corresponds to lectures, tutorials and lab sessions.
Indicative Assessment of Intended Learning Outcomes (1st session)
| Week | Individ./group | In-person/remote | Type of exam | Evaluated outcomes | Scale % |
|---|---|---|---|---|---|
| 7 ou plus | Individual | In-person | Written | AAV1 à AAV6 | 60% |
| 7 ou plus | Individual | In-person | Practical | AAV7 | 30% |
| 1 to 6 | Individual | Remote | Practical | AAV1 à AAV7 | 10% |
2nde session
| Session | Individ./group | In-person/remote | Type of exam | Evaluated outcomes | Scale % |
|---|---|---|---|---|---|
| 2 | Individual | In-person | Written | AAV1 to AAV6 | 60% |
| 1 | Individual | In-person | Practical | AAV7 | 30% |
| 1 | Individual | Remote | Practical | AAV1 à AAV7 | 10% |
Date of generation of this unit description: 14/01/2026
