Derivative Free Optimization / Optimisation sans Gradient

 

 (V04 course, season 2019/2020)

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, course 2018/2019


 Outline

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


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 : DIRECT, response surface methods  (RBF, kriging)


 Schedule : 

 

Friday 30th november 2019, 14h00-17h15 (ENSTA, A. Auger) DFO/STO/

Friday 14th décember 2019, 14h00-17h15 (ENSTA, A. Auger) DFO/STO/

Friday 21th décember2019, 14h00-17h15 (ENSTA, A. Auger) DFO/STO/

Friday 12th january 2020, 14h00-17h15 (ENSTA, A. Auger) DFO/STO/

Friday 17th january 2020, 14h00-17h15 (ENSTA, L. Dumas) : DFO/DET/

Friday 24th january 2020, 14h00-17h15 (ENSTA, A. Auger) : DFO/STO/

Friday  31th january 2020, 13h30-17h45 (ENSTA, L. Dumas) : DFO/DET/

Friday   7th february 2020, 13h30-17h45 (ENSTA, L. Dumas) : DFO/DET/

Friday 14th february 2020, 13h30-17h45 (ENSTA, L. Dumas): DFO/DET/


Friday 28th february 2020 14h00-17h00 (ENSTA): exam (text)


 Exercices : 

A list of exercises

 
 Scilab/ Matlab scripts : 

Pattern Search : pattern.sci

Nelder Nead : NelderMead.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)

Response surface methods : RBF.sci, krige.sce

 Bibliography : 

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

A review article on DFO : Journal of Global Optimization 2013

On direct search methods :

  1. The PhD thesis of Benoit Pauwels on DFO (2016) 

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

  3. An article on the convergence  of MDS:  PhD1989

  4. Convergence results for direct search methods (three references)

On trust region methods :

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

On global methods :

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

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

  3. A review article on response surface methods (RBF and kriging)

Other references :

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