# Optimization

mqant1329  2022-2023  Mons

Optimization
5.00 credits
30.0 h + 15.0 h
Q1
Teacher(s)
Language
English
Prerequisites

The prerequisite(s) for this Teaching Unit (Unité d’enseignement – UE) for the programmes/courses that offer this Teaching Unit are specified at the end of this sheet.
Main themes
This course, taught in English, introduces to the foundations of integer programming and combinatorial optimization as well as to the main computing techniques used to model and solve practical discrete optimization problems enojoying partitioning, coloring, routing, telecommunications, location, sustainable logistics and supply chain management features. Particularly emphasis is given to the development of problem solving skills as well as to the digitalization aspects, including among others, the ability to transform mathematical formulations of real problems into computer programs able to solve them.
Learning outcomes
 At the end of this learning unit, the student is able to : 1 This course contributes to develop the following competencies: KnowledgeScientific reasoning and systematic approachProject management and developmentLeadership At the end of this course, students will: Improve analytical and quantitative thinking skillsAcquire fundamental knowledge on the modeling, implementation, and the resolution of practical problemsApply the appropriate techniques to achieve meaningful solutions.Critically analyze the solution to take strategical decisions.
Content
This course, taught in English, introduces to the foundations of integer programming and combinatorial optimization as well as to the main computing techniques used to model and solve practical discrete optimization problems enojoying partitioning, coloring, routing, telecommunications, location, sustainable logistics and supply chain management features. Particularly emphasis is given to the development of problem solving skills as well as to the digitalization aspects, including among others, the ability to transform mathematical formulations of real problems into computer programs able to solve them.
Table of Contents: Mathematical Preliminaries; Fundamental problems in linear algebra and number theory; Optimizing over diophantine inequalities with positivity constraints; Optimality, relaxations families and relationships among relaxations, and type of bounds; Efficiently solvable combinatorial optimization problems; Rudiments of computational complexity; General solution approach to optimization over integers; Introduction to polyhedral combinatorics; Branch-and-cut; Fundations of the Mosel programming language and applications.
Teaching methods
Slided, Blackboard lectures, and Excercises in the Computing room.
Evaluation methods
Students are assessed individually by means of an exam that consists of two parts:

1. An evaluation of the applied modeling skills, which is usually carried out during the last session of the exercizes and which focuses on the Mosel programming language as well as on the ability to model given toy problems. This part is carried out only once per year and the participation is mandatory for all of the students. A poor score on this part precludes the access to the second part (see point 2).
2. An evaluation of the theoretical skills of the students, carried out by means of a written exam during the standard examination sessions.
In the case of a red code due to the COVID crisis, an oral will replace the written exam mentioned in point 2.
Online resources
Online resources are posted exclusively in the official channel of the course on Microsoft Teams.
Bibliography
The lectures will be integrated with some capita selecta from the following references: (1) S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge University Press 2004. (2) L. A. Wolsey. Integer Programming. Wiley Interscience, 1988. (3) M. Conforti, G. Cornuejols, G. Zambelli. Integer Programming. Springer, 2014. (4) Bagirov, M. Karmitsa and M. M. Mäkelä. Introduction to non smooth optimization. Springer 2014. (5) F. F. Clarke. Optimization and nonsmooth analysis, Siam 1987.
Teaching materials
• Teaching material will be posted in the online resources on Microsoft Teams
Faculty or entity

#### Programmes / formations proposant cette unité d'enseignement (UE)

Title of the programme
Sigle
Credits
Prerequisites
Learning outcomes
Bachelor : Business Engineering