Derivative Free Optimization / Optimisation sans Gradient

 (V04 course, season 2018/2019)

Common course between M2 AMS et M2 Optimisation (Paris Saclay)

 Anne Auger (INRIA), Laurent Dumas (UVSQ)

Optimization problems are encountered in many fields of engineering for which the associated cost function may be of various type : black box or explicit, with continuous or discrete variables, costly or not to compute, etc…

In many cases, the gradient of the cost function is not easy or even impossible to compute or it can exhibit many local minima leading to consider Derivative Free Optimization (DFO) methods.

This course deals with a large number of Derivative Free Optimization methods that have been recently developped, either local or global, deterministic or stochastic. It will be illustrated by various examples issued from industrial or medical fields.

 Previous courses :

 cours 2011/2012, cours 2012/2013, cours 2013/2014  cours 2014/2015 course 2015/2016 course 2016/2017, course 2017/2018

 Outline

-PART 1 : STOCHASTIC METHODS (see page of Anne Augier)

1) General introduction / Motivation for DFO

2) Stochastic algorithms framework (essentially ES)

3) General principles for step size and covariance matrix adaptation. CMA-ES algorithm.

4) Comparisons between CMA/PSO/NEWUOA/BFGS

-PARTIE 2 : DETERMINSTIC METHODS

1) Local methods: direct methods (Pattern Search, Nelder Mead, MDS), trust region methods (NEWUOA)

2) Global methods : response surface methods  (RBF, kriging), DIRECT

 Schedule : 

Vendredi 30 novembre 2018, 14h00-17h15 (ENSTA, A. Auger) DFO/STO/

Vendredi 07 décembre 2018, 14h00-17h15 (ENSTA, A. Auger) DFO/STO/

Vendredi 14 décembre 2018, 14h00-17h15 (ENSTA, A. Auger) DFO/STO/

Vendredi 21 décembre 2018, 14h00-17h15 (ENSTA, A. Auger) DFO/STO/

Vendredi 12 janvier 2019, 14h00-17h15 (ENSTA, A. Auger) DFO/STO/

Vendredi 18 janvier 2019, 14h00-17h15 (ENSTA, L. Dumas) : DFO/DET/direct methods

Vendredi 25 janvier 2019, 14h00-17h15 (ENSTA, L. Dumas) : DFO/DET/direct methods

Vendredi  1 février 2019, 14h00-17h15 (ENSTA, L. Dumas) : DFO/DET/trust region methods

Vendredi  8 février 2019, 14h00-17h15 (ENSTA, L. Dumas) : DFO/DET/trust region and global methods

Vendredi 15 février 2019, 14h00-17h15 (ENSTA, L. Dumas): soutenance des projets, partie 2 (planning)

Vendredi 22 février 2019 14h00-17h15 (ENSTA): évaluation écrite, partie 1

 Scilab/ Matlab scripts : 

Pattern Search : pattern.sci

Nelder Nead : NelderMead.sci

MDS: MDS.sci

A trust region method (with derivatives) : trust_noDFO.sci

A langrange interpolation script : lagrange_DFO.sci

A trust region method (without derivatives) : Trust.zip (in Matlab)

DIRECT method : DIRECT.zip (in Matlab)

 Bibliography : 

A. Conn, K. Scheinberg and L. Vincente, Introduction to Derivative Free Optimization, SIAM, 2009.

A review article on DFO : Journal of Global Optimization 2013

The PhD thesis of Benoit Pauwels on DFO (2016) 

An article on the non convergence of Nelder Mead : SIAM J. Opt.1998

An article on the convergence  of MDS:  PhD1989

An article on the SIR model (from A. Perasso)

Convergence results for direct search methods (three references)

An article on the convergence of Trust Region methods : SIAM Journal of Optimization, 2010

N. Gould, S. Leyffer, An introdution to algorithms for non linear optimization

The slides (in french) on Response Surface Methods (RBF  and kriging)

Description of the DIRECT method : DIRECT.pdf (Journal of Optimization theory and application, 1993)

A list of optimization test functions : http://www.sfu.ca/~ssurjano/optimization.html