Implementing finding alghoritm with for loops and fmincon function - matlab

Question

I am trying to implement this alghoritm for finding a new constraint:
In my case we take only 3 natural numbers i.e 1,2, 3.
The sets associated with those natural numbers are M1, M2 and M3. Instead of the Newton Method in II(2), I chose a solver provided by Matlab fmincon.
Here is my code that is not working!
function[s_new]= checking2(M1,M2,M3,x)
M1=linspace(0,1,10)';
M2=linspace(0,1,100)';
M3=linspace(0,1,1000)';
bool1=0;
eta = 10^-8;
pocz=[];
max=-100;
x = [0.1,0.1]'; % warunek początkowy
A = [];
b = [];
Aeq = [];
beq = [];
Set=[0,1];
g = #(x,s) 5*x(1).^2.*sin(pi.*sqrt(s))./(1+s.^2) - x(2);
g_new = #(s) -g(x,s);
for i=1:length(M1)
if g(x,M1(i,:))>eta
s_new=M1(i,:);
bool1=1;
end
end
if ~bool1
for i=1:length(M1)
if g(x,M1(i,:))>max
pocz=M1(i,:);
max=g(x,M1(i,:));
end
end
if max<-eta
bool1=1;
end
end
if ~bool1
s_maybe = fmincon(g_new,pocz,A,b,Aeq,beq,min(Set),max(Set));
if g(x,s_maybe)>eta
s_new=s_maybe;
bool1=1;
end
end
if ~bool1
for i=1:length(M2)
if g(x,M2(i,:))>eta
s_new=M2(i,:);
bool1=1;
end
end
end
if ~bool1
for i=1:length(M2)
if g(x,M2(i,:))>max
pocz=M2(i,:);
max=g(x,M2(i,:));
end
end
if max<-eta
bool1=1;
end
end
if ~bool1
s_maybe = fmincon(g_new,pocz,A,b,Aeq,beq,min(Set),max(Set));
if g(x,s_maybe)>eta
s_new=s_maybe;
bool1=1;
end
end
if ~bool1
for i=1:length(M3)
if g(x,M3(i,:))>eta
s_new=M3(i,:);
bool1=1;
end
end
end
if ~bool1
s_new = 1;
end
disp(s_new);
The problem is:
Undefined function or variable 's_new'.
Error in checking2 (line 70)
disp(s_new);
So basically everything might be wrong, but I suppose it is something with fmincon.
EDIT:
The purpose of the alghoritm is to find a minimum of an objective function f(x), satisfying all the constraints g(x,s)<=0 for all s in S, where S is an infinite set (some interval in our case).
What my alghoritm does, at first it takes some finite subset of S and calculates the minimum of f on this set, then I am trying to update S with some s_new. This alghoritm that I am trying to implement is exactly the procedure for creating s_new. Then if it works properly, I will add s_new to my subset and calculate the minimum on the new set, and so on until g(x,s)<=eta, where eta is a small number.

Answer 1

I rewrite the algorithm, read through the comments
clc
clear
lb = 0;
ub = 1;
% Given
l = 3;
M1=linspace(lb,ub,10)';
M2=linspace(lb,ub,100)';
M3=linspace(lb,ub,1000)';
% one boolean value for each Matrix
bool = zeros(1,3);
eta = 10^-8;
% Used as fmincon initial starting guess
pocz = nan;
% Used to store the new finding s that fits all the conditions
s_new = nan;
% Fixed x
x = [0.1,0]';
% fmincon linear constraints
A = [];
b = [];
Aeq = [];
beq = [];
% Main function
g = #(x,s) 5*x(1).^2*sin(pi*sqrt(s))/(1+s.^2) - x(2);
% Optimization concerns s only, don't include x as x is fixed
g_new = #(s) -g(x,s);
% Assuming the maximum is reached at the upper bound, used in(II)(2)
max_s = ub;
maxfun = g(x, max_s);
% Use a cell, for each iteration use a specific matrix M
M = {M1, M2, M3};
for j = 1: length(M)
% used in (II)(1)
check = 0;
step = 1;
% (I) step 1
for i = 1:length(M{j})
% Stopping criteria
if g(x, M{j}(i)) > eta
s_new = M{j}(i);
bool(j) = 1;
break;
else
% Function maximum value for next step (II)
if maxfun < g(x, M{j}(i))
maxfun = g(x, M{j}(i));
% To be used in fmincon as pocz
max_s = M{j}(i);
end
end
% To be used in (II)(1)
if maxfun < -eta
check = 1;
end
end
% End of (I)
% Put (II)(1) here step 2
if ~bool(j) && check
step = step + 1;
% Stopping criteria
if step >= l
disp('S_new not defined');
break;
end
% otherwise go to the next M
end
% (II)(2) step 3
if ~bool(j)
step = step + 1;
if maxfun >= -eta && maxfun <= eta
pocz = max_s;
bool(j) = 1;
end
end
%% EDIT: if bool(j) changed to if ~bool(j)
% (II)(2) Continue
if ~bool(j)
s_maybe = fmincon(g_new,pocz,A,b,Aeq,beq,lb,ub);
% End of (II)(2)
% (II)(2)-1 step 4
step = step + 1;
if g(x, s_maybe) > eta
s_new = s_maybe;
bool(j) = 1;
end
% End of (II)(2)-1
end
% Put (II)(2) here step 5
if ~bool(j)
step = step + 1;
% Stopping criteria
if step >= l
disp('S_new not defined');
break;
end
% otherwise go to the next M
end
end