[Scilab-users] 'optim' vs 'Nelder-Mead' ... or difficulties to use 'optim'

[paul.carrico at free.fr]

Hi all

Well, from a "macro" point of view, gradient based methods (order 1
method) should be more efficient than Nelder-Mead one (order 0)
especially  for 1D topic, shouldn't be?

In the case here bellow, when I use 'Optim' it is not the case in
comparison to 'NelderMead'... I don'y know what I'm doing wrong but I
decide to frop off 'optim' in favor tp Nelder-Mead - nevertheless the
later method requires much more iterations :-(

I'll be interested by some feedback on such topic, either in the mailing
list (or in MP in order to not pollute it).

Paul

########################################" 
'optim' 
######################################## 

mode(0)

function f=lineaire(x, a2, b2)
    f = a2*x+b2;
endfunction

function g=racine(x, a1, b1)
    g = sqrt(a1*x) + b1;
endfunction

function f=target(x)
    val_lin = lineaire(x,1,2);
    val_rac = racine(x,10,6);
    f = abs(val_lin - val_rac);
endfunction

// Cost function : 
function [f, g, ind]=cost(x, ind)
    f = target(x);   
//    g = numderivative(target, x.'); 
//    g = numderivative(target, x.',0.1,order = 2); 
    g = numderivative(target, x.',order = 2);  // better but why ??? h
automatic works better ???
//    g = numderivative(target, x.',order = 4); 
//    g = numderivative(target, x.',0.1, order = 4);
endfunction

// optimisation avec optim
    initial_parameters = [50]
    lower_bounds = [0];
    upper_bounds = [1000];
    nocf = 1000;      // number of call of f
    niter = 1000;    // number of iterations
    [fopt, xopt, gopt, work, iters, evals, err] =
optim(cost,'b',lower_bounds,upper_bounds,initial_parameters,'qn','ar',nocf,niter,imp=3);
    xopt
    fopt
    err

// traçage courbes
x = linspace(0,50,1000)';
plot_raci = racine(x,10,6);
plot_lin = lineaire(x,1,2);

scf(1);
drawlater();
xgrid(3);
f = gcf(); 
//f                                          
f.figure_size = [1000, 1000];                
f.background = color(255,255,255);           
a = gca();                                   
//a                                          
a.font_size = 2;                             
a.x_label.text = "X axis" ;                  
a.x_location="bottom";                       
a.x_label.font_angle=0;                      
a.x_label.font_size = 4;                     
a.y_label.text = "Y axis";
a.y_location="left";
a.y_label.font_angle=-90;
a.Y_label.font_size = 4;
a.title.text = "Title";                     
a.title.font_size = 5;
a.line_style = 1;    

// début des courbes
plot(x,plot_lin);
e1 = gce(); 
p1 = e1.children;                           
p1.thickness = 1;
p1.line_style = 1;
p1.foreground = 3;

plot(x,plot_raci);
e2 = gce(); 
p2 = e2.children;                           
p2.thickness = 1;
p2.line_style = 1;
p2.foreground = 2;
drawnow();

#######################################
Nelder Mead
#######################################

mode(0)

function f=lineaire(x, a2, b2)
    f = a2*x+b2;
endfunction

function g=racine(x, a1, b1)
    g = sqrt(a1*x) + b1;
endfunction

function [f, index]=target(x, index)
    val_lin = lineaire(x,1,2);
    val_rac = racine(x,10,6);
    f = abs(val_lin - val_rac);
endfunction

// optimisation avec optim
    initial_parameters = [50]
    lower_bounds = [0];
    upper_bounds = [1000];

nm = neldermead_new ();
nm = neldermead_configure(nm,"-numberofvariables",1);
nm = neldermead_configure(nm,"-function",target);
nm = neldermead_configure(nm,"-x0",initial_parameters);
nm = neldermead_configure(nm,"-maxiter",1000); 
nm = neldermead_configure(nm,"-maxfunevals",1000); 
nm = neldermead_configure(nm,"-tolfunrelative",10*%eps);
nm = neldermead_configure(nm,"-tolxrelative",10*%eps);
nm = neldermead_configure(nm,"-method","box");
nm = neldermead_configure(nm,"-boundsmin",lower_bounds);
nm = neldermead_configure(nm,"-boundsmax", upper_bounds);
nm = neldermead_search(nm);
nm = neldermead_restart(nm);
xopt = neldermead_get(nm,"-xopt")
fopt = neldermead_get(nm,"-fopt")
nm = neldermead_destroy(nm);

// traçage courbes
x = linspace(0,50,1000)';
a1 = 10; b1 = 6;  // b1 > b2 here
a2 = 1; b2 = 2;

plot_raci = racine(x,a1,b1);
plot_lin = lineaire(x,a2,b2);

scf(1);
drawlater();
xgrid(3);
f = gcf(); 
//f                                          
f.figure_size = [1000, 1000];                
f.background = color(255,255,255);           
a = gca();                                   
//a                                          
a.font_size = 2;                             
a.x_label.text = "X axis" ;                  
a.x_location="bottom";                       
a.x_label.font_angle=0;                      
a.x_label.font_size = 4;                     
a.y_label.text = "Y axis";
a.y_location="left";
a.y_label.font_angle=-90;
a.Y_label.font_size = 4;
a.title.text = "Title";                     
a.title.font_size = 5;
a.line_style = 1;    

// début des courbes
plot(x,plot_lin);
e1 = gce(); 
p1 = e1.children;                           
p1.thickness = 1;
p1.line_style = 1;
p1.foreground = 3;

plot(x,plot_raci);
e2 = gce(); 
p2 = e2.children;                           
p2.thickness = 1;
p2.line_style = 1;
p2.foreground = 2;
drawnow();
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