Optimization is a common form of decision making. Its applications range from solving game till daily life issues like ranging a wardrobe. The same problem-solving pattern can be used in multiple scenarios. In this class students will see how to apply mathematical and engineering methods to study and solve optimization problems.
The class will cover scalar and multidimensional optimization problems, with or without constraints, and a family of numerical methods to solve them. The class will implement and assess the performance of the presented methods to various real cases and applications of these theoretical properties: Business and Management, Economics, Data Science, and Energy Engineering.
Logistic informations regarding the course are summarized in [slides]. All the course materials will be made available online with EDUNAO platform.This lecture session introduces the concept of optimization problem modeling, through several motivating examples in the field of Data Science and Business Analytics.
This exercice session illustrates, on several examples, how to formulate an optimization problem given a concrete case description.
This lab session allows the students to get familiar with Python software, and NumPy library, through simple examples.
The first part of the lecture introduces the students to the analysis of optimization problems. The second part lecture introduces the students to the resolution of nonlinear programming problems using gradient-based approaches.
The first part of the session allow the students to perform the optimization problem analysis on practical examples in low dimension. The second part of the exercise session allows the students to practice gradient/Hessian calculation.
The lab session allows the students to discover and implement the golden bisection resolution technique, for scalar optimization under bound constraints, on concrete examples, using Python software.
The lecture introduces the students to the formulation and analysis of linear programming problems, and their practical resolution on simple examples.
The exercice session allows the students to formulate and solve linear programming problems on practical examples.
The lab session allows the students to implement gradient descent algorithm, using Python software, on a problem of binary classification.
The lecture introduces the students to the resolution of least squares problems. The exercice session allows the students to work on on practical examples of linear regression.
The session allows to recap all the notions seen in class, and correct quizz and exercices, in preparation for the exam.
The lab session allows the students to solve numerically linear regression problems, using Python software.
The class is splitted in three groups, for the lab sessions.
Lab reports must be sent to the TA, at the end of the lab session.
Please follow the instructions of your lab teacher regarding the file content and format.
No delay will be tolerated.