NUMERICAL OPTIMIZATION and APPLICATIONS (Electif 9, saison 2013)
Laurent DUMAS
Muhammad Zaid DAUHOO
Archives : course 2009 , 2010 , 2011, 2012
Course Objectives :
Many problems occuring in industry consist in minimizing (or maximizing) a certain
cost function. This course is aimed to present various optimization methods in
order to solve such problems.
After a general introduction on numerical optimization, various
optimization methods will be presented: derivative free optimization, descent-type
methods (gradient, newton, BFGS), evolutionary algorithms. A numerical
implementation with Scilab of these differents methods will be done during the
computer sessions.
Teachers : L . Dumas (Université de
Versailles), M.Z. Dauhoo (University of Mauritius)
Course prerequisites :
No specific prerequisites are needed for this course.
It is accessible with basic tools in analysis (functions of n variables).
Syllabus (see timetable
):
Mercredi 06 février
2013 (14-17h, LD):
introduction (lecture1.ppt), derivative free optimization (MDS.sci,
NelderMead.sci)
Vendredi 08 février
(8h-11h, MZD): steepest
descent method, Newton method
Mercredi 20 février
(14-17h, LD): linesearch
strategy, practical session with MATLAB/SCILAB (énoncé,
steepest.sci )
Vendredi 22 février
(8h-11h, MZD):
linear programming
Mercredi 27 février
(14-17h, LD): exercises+computer
session : linear programming (simplex.sci)
Vendredi 1 mars
(8h-11h, MZD): constrained
optimization : theory and algorithms
Vendredi 8 mars
(8h-11h,MZD):
constrained optimization : theory and algorithms
Vendredi 15 mars
(8h-11h, MZD): constrained
optimization : theory and algoithms
Mercredi 20 mars
(14-17h, LD):
simulated annealing (SA.sci), genetic algorithm (GA.sci,
GA-binary2011.sci), PSO (ECP2011-PSO.sci)
Examen le Vendredi 5 avril (énoncé)
References :
Livres:
Optimisation
continue : cours et exercices, J.F. Bonnans, Dunod, 2006.
Numercial optimization, theoretical and practical aspects : JF Bonnans, JC
Gilbert, C. Lemaréchal, C. Sagastizbal, Springer Verlag 2003.
Genetic
Algorithms on search, optimization and machine learning : D. Goldberg, 1989
Articles (online):
An
introdution to algorithms for non linear optimization : N. Gould, S.
Leyffer
Training :