sub-gradients - reg

clear all
close all 
clc 
f1=zeros(1,100); 
f2=zeros(1,100);
f3=zeros(1,200); 
c1=randi([1,20],1,100);
c2=randi([1,20],1,100); 
y(1,1:200)=rand(1,200); 
f1(1,1:100)=[y(1,1:100).*c1];
f2(1,1:100)=[y(1,101:200).*c2]; 
f3(1,1:200)=horzcat(f1,f2);
g1=zeros(1,100);
g2=zeros(1,100);
g1=gradient(f1,y(1:100));
g2=gradient(f2,y(101:200));
g=horzcat(g1,g2);

my question is whether g1 and g2 are sub-gradients of f1 and f2 respectively in the above code

[Walter Roberson]

What is a "sub-gradient" for this purpose?

Note: what you have is not exactly equivalent of

g = graient(f3, y(1:200))

There would be a difference due to boundary conditions. Compare

gradient([1 3 6 10 15])

to

[gradient([1 3 6]), gradient([10 15])]

[Siva]

i required the sub gradients to apply decomposition. without using 'g=horzcat (g1,g2)'. can i write the primal decomposition by using 'g1' and 'g2'.

[Walter Roberson]

What is a "sub gradient" ?

[Siva]

sub gradient method as used in lagrangian decomposition and lagrangian relaxation algorithms

Answer 1

[Walter Roberson]

my question is whether g1 and g2 are sub-gradients of f1 and f2 respectively in the above code

No. Lagrangian sub-gradient methods apply to functions, but you do not have functions.

gradient() applied to numeric matrices is numeric differences, and the second and following arguments give the step sizes.