Are the variables(fminimax) independent of each other?

in this code i have 68 variable half of them between [0,1] and next half [-90,90]

the first half change reasonable but others dont change (almost 0.3) and dont go to minus area

are they related to each other?

% close all
clear all

elementNumb=34;


%%
%%with W
% random_numbersw = rand(1,elementNumb);            % Random number from 0 to 1
random_numbersw = ones(1,elementNumb);
ubb=90;
lbb=-90;
% random_numberst = lbb + (ubb + ubb) * rand(1, elementNumb);        % Random number from -90 to 90
random_numberst =12* (ones(1 , elementNumb));
x0 = [ random_numbersw,random_numberst ] ;
ub = zeros(1, elementNumb*2);  % Initialize a matrix of zeros with 40 elements
ub(1:elementNumb) = 1;       % Set values from 1 to 21 to 0
ub(elementNumb+1:elementNumb*2) = ubb;     % Set values from 22 to 40 to 90
lb = zeros(1, elementNumb*2);  % Initialize a matrix of zeros with 40 elements
lb(1:elementNumb) = 0.000001;       % Set values from 1 to 21 to 0
lb(elementNumb+1:elementNumb*2) = lbb;    % Set values from 22 to 40 to 90

%%
%%Fminimax

% options = optimoptions(@fminimax,'disp','iter','Diagnostics',...
%     'on', 'FiniteDifferenceStepSize',1e-3,...
%     'FunctionTolerance',1e-9,'MaxFunctionEvaluations',20000,'FunValCheck','on','ConstraintTolerance',0);
% options = optimoptions(@fminimax,'disp','iter','Diagnostics',...
%     'on',...
%     'FunctionTolerance',1e-9,'MaxFunctionEvaluations',2000,'FunValCheck','on');
% % options=optimset('disp','iter','LargeScale','off','Diagnostics',...
%     'on','TolFun',.00000000000001,'MaxIter',10000,'MaxFunEvals',1000000);
[x,fval,maxfval,exitflag,output,lambda] = fminimax(@costy,x0,[],[],[],[],lb,ub,[]);

%%function
function y = costy(x)

freq = 9*10^9;       %Freq
j = sqrt(-1);        %Define Imaginary
l =(3*10^8)/freq;    %Lambda
k = (2*pi)/l;        %Constant
d = 0.5*l;           %Distant of each element
elementNumb = 34;
step = 0.1;

teta1 = ((-80)  :step:  (-50));


tetat = teta1;



g = zeros(elementNumb,length(tetat));

    for h = 1:elementNumb
        
        for aa = 1:length(teta1)
              
        g(h,aa) = g(h,aa)+(x(h) * ( exp(-j*(h-1) * (k*d*sind(teta1(aa)+x(h+elementNumb))))));      %w W
        end
        
    end

y = abs(sum(g,1));

    
 end

and can they change with certain step for example first half 0.01 and second 5

[Walter Roberson]

x(h+elementNumb)=x(h+elementNumb);

What is the benefit of that line of code?

[koorosh dastan]

I edit that

I try to double check my code for next

[Walter Roberson]

You need to permit more iterations

elementNumb=34;


%%
%%with W
% random_numbersw = rand(1,elementNumb);            % Random number from 0 to 1
random_numbersw = ones(1,elementNumb);
ubb=90;
lbb=-90;
% random_numberst = lbb + (ubb + ubb) * rand(1, elementNumb);        % Random number from -90 to 90
random_numberst =12* (ones(1 , elementNumb));
x0 = [ random_numbersw,random_numberst ] ;
ub = zeros(1, elementNumb*2);  
ub(1:elementNumb) = 1;       
ub(elementNumb+1:elementNumb*2) = ubb;     
lb = zeros(1, elementNumb*2);  
lb(1:elementNumb) = 0.03125;      
lb(elementNumb+1:elementNumb*2) = lbb;    

%%
%%Fminimax

% options = optimoptions(@fminimax,'disp','iter','Diagnostics',...
%     'on', 'FiniteDifferenceStepSize',1e-3,...
%     'FunctionTolerance',1e-9,'MaxFunctionEvaluations',20000,'FunValCheck','on','ConstraintTolerance',0);
% options = optimoptions(@fminimax,'disp','iter','Diagnostics',...
%     'on','FiniteDifferenceStepSize',0.03125,...
%     'FunctionTolerance',1e-9,'MaxFunctionEvaluations',2000,'FunValCheck','on');
% % options=optimset('disp','iter','LargeScale','off','Diagnostics',...
%     'on','TolFun',.00000000000001,'MaxIter',10000,'MaxFunEvals',1000000);
options = optimoptions(@fminimax, 'MaxFunctionEvaluations', 20000, 'FunValCheck', 'on');
[x,fval,maxfval,exitflag,output,lambda] = fminimax(@costy,x0,[],[],[],[],lb,ub,[],options)

Local minimum possible. Constraints satisfied.

fminimax stopped because the predicted change in the objective function
is less than the value of the function tolerance and constraints 
are satisfied to within the value of the constraint tolerance.

x = 1×68

0.0312 0.1603 0.4457 0.7698 0.9373 0.8714 0.7723 0.8110 0.9235 0.9144 0.8142 0.7950 0.9053 0.9845 0.8910 0.7986 0.8727 0.9780 0.9017 0.8312 0.8588 0.9048 0.9441 0.9236 0.8945 0.9359 0.9057 0.8616 0.8217 0.9628

fval = 1×301

1.0e-04 * 0.8228 0.5679 0.3519 0.2019 0.1991 0.3050 0.4229 0.5287 0.6181 0.6903 0.7459 0.7858 0.8111 0.8230 0.8226 0.8113 0.7902 0.7607 0.7240 0.6816 0.6348 0.5853 0.5349 0.4857 0.4403 0.4017 0.3734 0.3583 0.3583 0.3728

maxfval = 8.2763e-05

exitflag = 5

output = struct with fields:
         iterations: 172
          funcCount: 12614
       lssteplength: 1
           stepsize: 9.9380e-04
          algorithm: 'active-set'
      firstorderopt: []
    constrviolation: 5.5519e-07
            message: 'Local minimum possible. Constraints satisfied.↵↵fminimax stopped because the predicted change in the objective function↵is less than the value of the function tolerance and constraints ↵are satisfied to within the value of the constraint tolerance.↵↵<stopping criteria details>↵↵Optimization stopped because the predicted change in the objective function,↵3.087656e-07, is less than options.FunctionTolerance = 1.000000e-06, and the maximum constraint↵violation, 5.551912e-07, is less than options.ConstraintTolerance = 1.000000e-06.'

lambda = struct with fields:
         lower: [68×1 double]
         upper: [68×1 double]
         eqlin: [0×1 double]
      eqnonlin: [0×1 double]
       ineqlin: [0×1 double]
    ineqnonlin: [0×1 double]

[small, high] = bounds(x(elementNumb+1:end))

small = 11.4138

high = 12.0653

%%function
function y = costy(x)

freq = 9*10^9;       %Freq
j = sqrt(-1);        %Define Imaginary
l =(3*10^8)/freq;    %Lambda
k = (2*pi)/l;        %Constant
d = 0.5*l;           %Distant of each element
elementNumb = 34;
step = 0.1;

teta1 = ((-80)  :step:  (-50));


tetat = teta1;



g = zeros(elementNumb,length(tetat));

    for h = 1:elementNumb
x(h+elementNumb)=x(h+elementNumb);
        
        for aa = 1:length(teta1)
              
        g(h,aa) = g(h,aa)+(x(h) * ( exp(-j*(h-1) * (k*d*sind(teta1(aa)+x(h+elementNumb))))));      %w W
        end
        
    end

y = abs(sum(g,1));

    
 end

[Walter Roberson]

Note, however, that these fval are several orders of magnitude worse than the original fvals.

elementNumb=34;


%%
%%with W
rng(65432);

random_numbersw = rand(1,elementNumb);            % Random number from 0 to 1
%random_numbersw = ones(1,elementNumb);
ubb=90;
lbb=-90;
random_numberst = lbb + (ubb + ubb) * rand(1, elementNumb);        % Random number from -90 to 90
%random_numberst =12* (ones(1 , elementNumb));
x0 = [ random_numbersw,random_numberst ] ;
ub = zeros(1, elementNumb*2);  
ub(1:elementNumb) = 1;       
ub(elementNumb+1:elementNumb*2) = ubb;     
lb = zeros(1, elementNumb*2);  
lb(1:elementNumb) = 0.03125;      
lb(elementNumb+1:elementNumb*2) = lbb;    

%%
%%Fminimax

% options = optimoptions(@fminimax,'disp','iter','Diagnostics',...
%     'on', 'FiniteDifferenceStepSize',1e-3,...
%     'FunctionTolerance',1e-9,'MaxFunctionEvaluations',20000,'FunValCheck','on','ConstraintTolerance',0);
% options = optimoptions(@fminimax,'disp','iter','Diagnostics',...
%     'on','FiniteDifferenceStepSize',0.03125,...
%     'FunctionTolerance',1e-9,'MaxFunctionEvaluations',2000,'FunValCheck','on');
% % options=optimset('disp','iter','LargeScale','off','Diagnostics',...
%     'on','TolFun',.00000000000001,'MaxIter',10000,'MaxFunEvals',1000000);
options = optimoptions(@fminimax, 'MaxFunctionEvaluations', 1e6, 'FunValCheck', 'on');
[x,fval,maxfval,exitflag,output,lambda] = fminimax(@costy,x0,[],[],[],[],lb,ub,[],options)

Local minimum possible. Constraints satisfied.

fminimax stopped because the predicted change in the objective function
is less than the value of the function tolerance and constraints 
are satisfied to within the value of the constraint tolerance.

x = 1×68

0.0972 0.5383 0.1354 0.9782 0.1019 0.0312 1.0000 0.0315 0.2759 0.1363 0.2511 0.0383 0.4076 0.3231 0.1660 0.9462 0.0689 0.8245 0.7678 1.0000 0.3905 0.6368 0.5186 0.2140 0.6079 0.0312 0.0457 0.5096 0.0312 1.0000

fval = 1×301

0.0160 0.0041 0.0053 0.0112 0.0146 0.0160 0.0157 0.0140 0.0114 0.0084 0.0056 0.0045 0.0062 0.0089 0.0114 0.0135 0.0150 0.0159 0.0160 0.0155 0.0144 0.0129 0.0110 0.0091 0.0074 0.0065 0.0069 0.0082 0.0100 0.0118

maxfval = 0.0160

exitflag = 5

output = struct with fields:
         iterations: 341
          funcCount: 24543
       lssteplength: 1
           stepsize: 0.0155
          algorithm: 'active-set'
      firstorderopt: []
    constrviolation: 8.2747e-07
            message: 'Local minimum possible. Constraints satisfied.↵↵fminimax stopped because the predicted change in the objective function↵is less than the value of the function tolerance and constraints ↵are satisfied to within the value of the constraint tolerance.↵↵<stopping criteria details>↵↵Optimization stopped because the predicted change in the objective function,↵8.003316e-07, is less than options.FunctionTolerance = 1.000000e-06, and the maximum constraint↵violation, 8.274655e-07, is less than options.ConstraintTolerance = 1.000000e-06.'

lambda = struct with fields:
         lower: [68×1 double]
         upper: [68×1 double]
         eqlin: [0×1 double]
      eqnonlin: [0×1 double]
       ineqlin: [0×1 double]
    ineqnonlin: [0×1 double]

[small, high] = bounds(x(elementNumb+1:end))

small = -86.6930

high = 86.8862

%%function
function y = costy(x)

freq = 9*10^9;       %Freq
j = sqrt(-1);        %Define Imaginary
l =(3*10^8)/freq;    %Lambda
k = (2*pi)/l;        %Constant
d = 0.5*l;           %Distant of each element
elementNumb = 34;
step = 0.1;

teta1 = ((-80)  :step:  (-50));


tetat = teta1;



g = zeros(elementNumb,length(tetat));

    for h = 1:elementNumb
x(h+elementNumb)=x(h+elementNumb);
        
        for aa = 1:length(teta1)
              
        g(h,aa) = g(h,aa)+(x(h) * ( exp(-j*(h-1) * (k*d*sind(teta1(aa)+x(h+elementNumb))))));      %w W
        end
        
    end

y = abs(sum(g,1));

    
 end