NUMERICAL OPTIMIZATION and APPLICATIONS (Electif 9, saison 2012)
Laurent DUMAS
Muhammad Zaid DAUHOO
Tahar BOULMEZAOUD
Archives : course 2009 , 2010 , 2011
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: deterministic direct search
(Nelder Mead, simplex), descent-type methods (gradient, newton, BFGS),
stochastic methods (genetic algorithms, evolution strategies, PSO). A numerical
implementation with Scilab of these differents methods will be done during the
computer sessions.
Teachers : L . Dumas , T.
Z. Boulmezaoud (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 01 février 2012
(14-17h, TZB):
introduction, convexity
Vendredi 03 février (8h-11h,
LD): derivative
free optimization (DFO) (slides, directFBG.sci, NelderMead.sci,
MDS.sci)
Mercredi 15 février (14-17h,
TZB): optimality
conditions 1
Vendredi 17 février (8h-11h,
MZD): descent
algorithms 1
Mercredi 22 février (14-17h,
TZB): optimality
conditions 2
Vendredi 24 février (8h-11h,
MZD): descent
algorithms 2
Mercredi 29 février (14-17h,
MZD): exercices +
computer session : descent algorithms (TD,
TP)
Vendredi 02 mars
(8h-11h,LD):
evolutionary algorithms (SA.sci, ECP2012-GA.m, JJ.m)
Mercredi 07 mars (14-17h,
TZB): linear
programming
Vendredi 09 mars (8h-11h,
LD): evolutionary
algorithms (ECP2012-SR.sci)
Mercredi 14 mars (14-17h,
MZD): exercises+omputer
session : linear programming
Examen le Vendredi 30 mars
2012 (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 :