Teacher(s)
Language
English
Prerequisites
- MQANT1110 - Mathématiques de gestion 1
- MQANT1227 - Mathématiques de gestion 2
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
Part I (Continuous Optimization):
Continuity, differentiability in n dimension, conditions for differentiability, necessary conditions for optimality, convex sets, convex functions, convex optimization problems, Lagrangian duality, descent methods, rudiments of smooth and non-smooth nonlinear optimization;
Part II (Discrete Optimization):
Introduction to integer and combinatorial optimization; formulations; optimality, relaxations, and relationships among relaxations; well-solved problems; matchings and assignments; branch and bound;
Continuity, differentiability in n dimension, conditions for differentiability, necessary conditions for optimality, convex sets, convex functions, convex optimization problems, Lagrangian duality, descent methods, rudiments of smooth and non-smooth nonlinear optimization;
Part II (Discrete Optimization):
Introduction to integer and combinatorial optimization; formulations; optimality, relaxations, and relationships among relaxations; well-solved problems; matchings and assignments; branch and bound;
Learning outcomes
At the end of this learning unit, the student is able to : | |
| 1 | This course contributes to develop the following competencies :
Locate and identify free extrema of a function; locate extrema under constraints of a function using the technique of Lagrange multipliers. Understand and learn the foundations of continuous and discrete optimization and the main computing techniques to tackle an optimization problem. |
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.
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
Interactive whiteboard lectures and excercises in the computing rooms.
Evaluation methods
The evaluation for this course is governed by Article 78 of the RGEE and follows a "unique" format. It involves both an evaluation in itinere and the resolution of one or more optimization case studies whose requirements and specifications may potentially vary each year. The evaluation in itinere can contribute up to 60% of the final grade, while the case studies may contribute up to 40%. These percentage are indicative and may be adjusted annually. Full details, including any adjustments, are provided by the lecturer during the first mandatory class session.
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) L. A. Wolsey. Integer Programming. Wiley Interscience, 2021.
(2) M. Conforti, G. Cornuejols, G. Zambelli. Integer Programming. Springer, 2014.
(3) S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge University Press 2004.
(1) L. A. Wolsey. Integer Programming. Wiley Interscience, 2021.
(2) M. Conforti, G. Cornuejols, G. Zambelli. Integer Programming. Springer, 2014.
(3) S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge University Press 2004.
Teaching materials
- Teaching material will be posted in the online resources on Microsoft Teams
Faculty or entity
