5 credits
30.0 h + 15.0 h
Q1
Teacher(s)
Catanzaro Daniele; Meskens Nadine;
Language
English
Prerequisites
- MQANT1110 - Mathématiques de gestion 1
- MQANT1227 - Mathématiques de gestion 2
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;
Aims
At the end of this learning unit, the student is able to : | |
| 1 | This course contributes to develop the following competencies :
Study limits, continuity, directional derivatives and differentiability for functions of several variables. 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. |
The contribution of this Teaching Unit to the development and command of the skills and learning outcomes of the programme(s) can be accessed at the end of this sheet, in the section entitled “Programmes/courses offering this Teaching Unit”.
Content
- Limits, continuity and continuous extension for functions of several variables
- Directional derivative, differentiation, tangent plane and Jacobian matrix
- Partial derivatives of higher order and Taylor polynomials
- Fermat's theorem, free extrema and extrema under constraints
- Convex sets, convex functions, convex optimization problems, Lagrangian duality
- Descent methods, rudiments of smooth and non-smooth nonlinear optimization
- Introduction to integer and combinatorial optimization, formulations, optimality, relaxations, and relationships among relaxations
- well-solved problems
- matchings and assignments
- branch and bound
Teaching methods
Blackboard lectures.
Evaluation methods
Students are assessed individually in order to test the competences announced above.
The final written exam involves both (i) solving exercises similar to those proposed during the course and the tutorials and (ii) understanding and applying the theory to a specific case.
The final written exam involves both (i) solving exercises similar to those proposed during the course and the tutorials and (ii) understanding and applying the theory to a specific case.
Faculty or entity
CLSM
