should cost function be only one point?

should cost function be only one point?

assume I have numerous points to minimize, where I can change the values of these points. For example, I want to sweep from 90 to -90 with a step of 0.2 or 0.1, etc. Is it better to try an algorithm that attempts to minimize and maximize all points, or should I write a cost function and then try to work on it? Below, you can see a part of the code related to this.

or i must only have one point ????

be

first approach (alot of point)

and pls attention in teta3 here (where i like my func be max try to inverse it) in the end

(1./b(sumLenteta12+1:sumLenteta123))

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 = 0.67*l;           %Distant of each element
elementNumb = 34;
step = 0.5;

teta1 = ((-70)  :step:  (-40));
teta2 = ((-40)  :step:  (6));
teta3 = ((11)    :step:  (15));
teta4 = ((18)   :step:  (45));
teta5 = ((45)   :step:  (60));

tetat = [teta1,teta2,teta3,teta4,teta5];
lenteta1 = length(teta1);
sumLenteta12   = length(teta1) + length(teta2);
sumLenteta123  = length(teta3) + sumLenteta12;
sumLenteta1234 = sumLenteta123 + length(teta4);
g = zeros(elementNumb,length(tetat));
ww=90;
    for h = 1:elementNumb

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

        %%teta2
        for bb=(lenteta1+1):(sumLenteta12)
        

        g(h,bb) =g(h,bb)+( x(h) * exp(j*(h-1) * (k*d*sind(teta2(bb-lenteta1)+(ww*x(h+elementNumb)))))); %with W
        end

        %%teta3

        for cc = (sumLenteta12+1):(length(teta3)+sumLenteta12)
       

        g(h,cc) = g(h,cc)+ (x(h) * exp(j*(h-1) * (k*d*sind(teta3(cc-sumLenteta12)...
            +(ww*x(h+elementNumb))))));  %w W  
     
        end

        %%teta4

         for dd = (sumLenteta123+1):(sumLenteta123+length(teta4))
 

          g(h,dd) = g(h,dd)+( x(h) * exp(j*(h-1) * (k*d*sind(teta4(dd-(sumLenteta123))...
                 +(ww*x(h+elementNumb))))));  %w W           

          end
        %%teta5

         for ee = (sumLenteta1234+1):(sumLenteta1234+length(teta5))


             g(h,ee) = g(h,ee)+( x(h) * exp(j*(h-1) * (k*d*sind(teta5(ee-(sumLenteta1234))...
                 +(ww*x(h+elementNumb))))));  %w W
         end
         % disp([x(1),x(2),x(3),x(35),x(36),x(50)]);
    end
%for weighting
w1 = 0;
w2 = 0;
w3 = 0;
w4 = 0;
w5 = 0;
b = abs(sum(g));
% b=b/max(b);
% b=20*log10(abs(b));
% for each point evaluate    
b = [b(1:lenteta1)+w1,b(lenteta1+1:sumLenteta12)+w2,(1./b(sumLenteta12+1:sumLenteta123))+w3 ... 
    ,b(sumLenteta123+1:sumLenteta1234)+w4,b(sumLenteta1234+1:length(tetat))+w5];
y = b;
end

and one point here i get from each one max then try to minimize it

and attention here i add minus for max (teta3)

b3 = -max(b(sumLenteta12+1:sumLenteta123))+w3 ;

and this one wants more time

and formula which i use

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 = 0.67*l;           %Distant of each element
elementNumb = 34;
step = 0.5;

teta1 = ((-70)  :step:  (-40));
teta2 = ((-40)  :step:  (6));
teta3 = ((11)    :step:  (15));
teta4 = ((18)   :step:  (45));
teta5 = ((45)   :step:  (60));

tetat = [teta1,teta2,teta3,teta4,teta5];
lenteta1 = length(teta1);
sumLenteta12   = length(teta1) + length(teta2);
sumLenteta123  = length(teta3) + sumLenteta12;
sumLenteta1234 = sumLenteta123 + length(teta4);

g = zeros(elementNumb,length(tetat));
ww=90;
    for h = 1:elementNumb

        %%teta1
        for aa = 1:length(teta1)

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

        %%teta2
        for bb=(lenteta1+1):(sumLenteta12)
    

        g(h,bb) =g(h,bb)+( x(h) * exp(j*(h-1) * (k*d*sind(teta2(bb-lenteta1)+(ww*x(h+elementNumb)))))); %with W
        end

        %%teta3

        for cc = (sumLenteta12+1):(length(teta3)+sumLenteta12)


        g(h,cc) = g(h,cc)+ (x(h) * exp(j*(h-1) * (k*d*sind(teta3(cc-sumLenteta12)...
            +(ww*x(h+elementNumb))))));  %w W  

        end

        %%teta4

         for dd = (sumLenteta123+1):(sumLenteta123+length(teta4))


          g(h,dd) = g(h,dd)+( x(h) * exp(j*(h-1) * (k*d*sind(teta4(dd-(sumLenteta123))...
                 +(ww*x(h+elementNumb))))));  %w W           

          end
        %%teta5

         for ee = (sumLenteta1234+1):(sumLenteta1234+length(teta5))


             g(h,ee) = g(h,ee)+( x(h) * exp(j*(h-1) * (k*d*sind(teta5(ee-(sumLenteta1234))...
                 +(ww*x(h+elementNumb))))));  %w W
         end
         % disp([x(1),x(2),x(3),x(35),x(36),x(50)]);
    end


w1 = 0;
w2 = 0;
w3 = 0;
w4 = 0;
w5 = 0;


b = abs(sum(g));
% b=b/max(b);
% b=20*log10(abs(b));
%% for each point evaluate    
% b = [b(1:lenteta1)+w1,b(lenteta1+1:sumLenteta12)+w2,(1./b(sumLenteta12+1:sumLenteta123))+w3 ... 
%     ,b(sumLenteta123+1:sumLenteta1234)+w4,b(sumLenteta1234+1:length(tetat))+w5];
% y = b;

%% for one point evaluate
b1 = max(b(1:lenteta1))+w1;
b2 = max(b(lenteta1+1:sumLenteta12))+w2;
b3 = -max(b(sumLenteta12+1:sumLenteta123))+w3 ; 
b4 = max(b(sumLenteta123+1:sumLenteta1234))+w4;
b5 = max(b(sumLenteta1234+1:length(tetat)))+w5;
totb=b1+b2+b3+b4+b5;
y = totb;
end

[Sam Chak]

Hi @koorosh dastan

I tested one of your cost functions, and it is unable to return a scalar value. Is the cost function supposed to represent a 5-variable manifold-valued curve, something like . Or, are you trying to optimize the cost function only for ?

x = [-55 -17 13 30 52];     % [θ1, θ2, θ3, θ4, θ5]
y = costy(x)                % a scalar value is expected

Index exceeds the number of array elements. Index must not exceed 5.

Error in solution>costy (line 32)
g(h,aa) = g(h,aa)+(x(h) * ( exp(j*(h-1) * (k*d*sind(teta1(aa)+(ww*x(h+elementNumb))))))); %w W

%% Dastan Cost 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    = 0.67*l;           %Distant of each element
    elementNumb = 34;
    step = 0.5;
    
    teta1 = -70:step:-40;   % θ1 range
    teta2 = -40:step:6;     % θ2 range
    teta3 =  11:step:15;    % θ3 range
    teta4 =  18:step:45;    % θ4 range
    teta5 =  45:step:60;    % θ5 range
    
    tetat          = [teta1, teta2, teta3, teta4, teta5];
    lenteta1       = length(teta1);
    sumLenteta12   = length(teta1) + length(teta2);
    sumLenteta123  = length(teta3) + sumLenteta12;
    sumLenteta1234 = sumLenteta123 + length(teta4);
    
    g  = zeros(elementNumb, length(tetat));
    ww = 90;
        for h = 1:elementNumb    
            %%teta1
            for aa = 1:length(teta1)
                g(h,aa) = g(h,aa)+(x(h) * ( exp(j*(h-1) * (k*d*sind(teta1(aa)+(ww*x(h+elementNumb)))))));      %w W
            end
            %%teta2
            for bb=(lenteta1+1):(sumLenteta12)
                g(h,bb) = g(h,bb)+( x(h) * exp(j*(h-1) * (k*d*sind(teta2(bb-lenteta1)+(ww*x(h+elementNumb)))))); %with W
            end    
            %%teta3
            for cc = (sumLenteta12+1):(length(teta3)+sumLenteta12)
                g(h,cc) = g(h,cc)+ (x(h) * exp(j*(h-1) * (k*d*sind(teta3(cc-sumLenteta12) +(ww*x(h+elementNumb))))));  %w W
            end    
            %%teta4    
            for dd = (sumLenteta123+1):(sumLenteta123+length(teta4))
                g(h,dd) = g(h,dd)+( x(h) * exp(j*(h-1) * (k*d*sind(teta4(dd-(sumLenteta123)) + (ww*x(h+elementNumb))))));  %w W           
            end
            %%teta5
            for ee = (sumLenteta1234+1):(sumLenteta1234+length(teta5))
                g(h,ee) = g(h,ee)+( x(h) * exp(j*(h-1) * (k*d*sind(teta5(ee-(sumLenteta1234)) + (ww*x(h+elementNumb))))));  %w W
            end
            % disp([x(1),x(2),x(3),x(35),x(36),x(50)]);
        end
    w1 = 0;
    w2 = 0;
    w3 = 0;
    w4 = 0;
    w5 = 0;
    
    b = abs(sum(g));
    % b=b/max(b);
    % b=20*log10(abs(b));
    %% for each point evaluate    
    % b = [b(1:lenteta1)+w1,b(lenteta1+1:sumLenteta12)+w2,(1./b(sumLenteta12+1:sumLenteta123))+w3 ... 
    %     ,b(sumLenteta123+1:sumLenteta1234)+w4,b(sumLenteta1234+1:length(tetat))+w5];
    % y = b;
    
    %% for one point evaluate
    b1   =  max(b(1:lenteta1))+w1;
    b2   =  max(b(lenteta1+1:sumLenteta12))+w2;
    b3   = -max(b(sumLenteta12+1:sumLenteta123))+w3 ; 
    b4   =  max(b(sumLenteta123+1:sumLenteta1234))+w4;
    b5   =  max(b(sumLenteta1234+1:length(tetat)))+w5;
    totb = b1 + b2 + b3 + b4 + b5;
    y    = totb;
end

[koorosh dastan]

thank you for your attention

i explain in below topic more about code

https://www.mathworks.com/matlabcentral/answers/2057934-fminimax-instead-decrease-increase-my-costfunct?s_tid=srchtitle

but there my code has some mistake like i should scale 90 to -90 and ...

i have 64 variavble in my function (x is my variable)

here is my complete code and if you like you can change my option i think itsnt good option

% close all
clear all
t0 = tic();
elementNumb=34;

%%
%%with W
% random_numbersw = rand(1,elementNumb);            % Random number from 0 to 1
random_numbersw = ones(1,elementNumb);
ubb=1;
lbb=-1;
% random_numberst = lbb + (ubb + ubb) * rand(1, elementNumb);        % Random number from -90 to 90
% random_numberst = 0.134*(ones(1 , elementNumb));
random_numberst =-0.145*(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) = 0.03125;       % 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,'MaxFunctionEvaluations', 1e6,'FunctionTolerance',1e-15,	...
%     'MaxIterations',1e3,'OptimalityTolerance',1e-10, 'MaxSQPIter',inf,'ConstraintTolerance',1e-9,'FunValCheck', 'on');
 options = optimoptions(@fminimax,'MaxFunctionEvaluations', 1e6,'FunctionTolerance',1e-15,	...
    'MaxIterations',1e4,'OptimalityTolerance',1e-10,'ConstraintTolerance',1e-9,'FunValCheck', 'on'); 
[x,fval,maxfval,exitflag,output,lambda] = fminimax(@costy,x0,[],[],[],[],lb,ub,[],options);
dt = toc(t0)
beep;
beep;
%% with non linear constraint
% [x,fval,maxfval,exitflag,output,lambda] = fminimax(@costy,x0,[],[],[],[],lb,ub,@nonlcon,options);
%%
%%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 = 0.67*l;           %Distant of each element
elementNumb = 34;
step = 0.5;

teta1 = ((-55)  :step:  (-25));
teta2 = ((-40)  :step:  (9));
teta3 = ((11)    :step:  (15));
teta4 = ((18)   :step:  (22));
teta5 = ((22)   :step:  (55));

tetat = [teta1,teta2,teta3,teta4,teta5];
lenteta1 = length(teta1);
sumLenteta12   = length(teta1) + length(teta2);
sumLenteta123  = length(teta3) + sumLenteta12;
sumLenteta1234 = sumLenteta123 + length(teta4);

g = zeros(elementNumb,length(tetat));
ww=90;
    for h = 1:elementNumb

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

        %%teta2
        for bb=(lenteta1+1):(sumLenteta12)
        % g(h,bb) =(g(h,bb)+( 1 * exp(-j*(h-1) * (k*d*sind(teta2(bb-lenteta1)+deltaTeta(h))))))-0.001; %w/o W

        g(h,bb) =g(h,bb)+( x(h) * exp(j*(h-1) * (k*d*sind(teta2(bb-lenteta1)+(ww*x(h+elementNumb)))))); %with W
        end

        %%teta3

        for cc = (sumLenteta12+1):(length(teta3)+sumLenteta12)
        % g(h,cc) = (g(h,cc)+( 1 * exp(j*(h-1) * (k*d*sind(teta3(cc-sumLenteta12)+deltaTeta(h))))))+0.01;  %w/o W

        g(h,cc) = g(h,cc)+ (x(h) * exp(j*(h-1) * (k*d*sind(teta3(cc-sumLenteta12)...
            +(ww*x(h+elementNumb))))));  %w W  
        % disp(g(10,sumLenteta12+1))
        end

        %%teta4

         for dd = (sumLenteta123+1):(sumLenteta123+length(teta4))
             % g(h,dd) = g(h,dd)+( 1 * exp(j*(h-1) * (k*d*sind(teta4(dd-(sumLenteta123))...
             %     +deltaTeta(h)))))+0.01;  %w/o W

          g(h,dd) = g(h,dd)+( x(h) * exp(j*(h-1) * (k*d*sind(teta4(dd-(sumLenteta123))...
                 +(ww*x(h+elementNumb))))));  %w W           

          end
        %%teta5

         for ee = (sumLenteta1234+1):(sumLenteta1234+length(teta5))


             g(h,ee) = g(h,ee)+( x(h) * exp(j*(h-1) * (k*d*sind(teta5(ee-(sumLenteta1234))...
                 +(ww*x(h+elementNumb))))));  %w W
         end
         % disp([x(1),x(2),x(3),x(35),x(36),x(50)]);
    end


w1 = 0;
w2 = 0;
w3 = 0;
w4 = 0;
w5 = 0;


b = abs(sum(g));
% b=b/max(b);
% b=20*log10(abs(b));
%% for each point evaluate    
% b = [b(1:lenteta1)+w1,b(lenteta1+1:sumLenteta12)+w2,(1./b(sumLenteta12+1:sumLenteta123))+w3 ... 
%     ,b(sumLenteta123+1:sumLenteta1234)+w4,b(sumLenteta1234+1:length(tetat))+w5];
% y = b;

%% for one point evaluate
b1 = max(b(1:lenteta1))+w1;
b2 = max(b(lenteta1+1:sumLenteta12))+w2;
b3 = max(b(sumLenteta12+1:sumLenteta123))+w3; 
b4 = max(b(sumLenteta123+1:sumLenteta1234))+w4;
b5 = max(b(sumLenteta1234+1:length(tetat)))+w5;
totb=b1+b2-b3+b4+b5;
y = totb;

end

and if you want to see result you can excute below code

you should open below code in another page and after excute previous code you get x

% function y = costy(teta)
    elementNumb=34;

Function definitions in a script must appear at the end of the file.
Move all statements after the "costy" function definition to before the first local function definition.

    deltaTeta=x(1:elementNumb*2);

    f=9*10^9;
    j=sqrt(-1);
    l=(3*10^8)/f;
    k=(2*pi)/l;
    d=0.67*l;
%     xas=90;
%     teta=((-1*xas):0.1:(1*xas));
    teta=((-1*90):0.1:(1*90));
%     deltaTeta=zeros(elementNumb)-11;
    y=0;
    % w=ones(elementNumb);
    for h=1:elementNumb

        % y=y+exp(j*(h-1)*(k*d*sind(teta)));
        y=y+deltaTeta(h)*exp(j*(h-1)*(k*d*sind(teta+90*deltaTeta(h+elementNumb))));

    end
y=y/max(y);
% end
figure;
% 
plot(teta,20*log10(abs(y)),'o')
% 
axis([-100 100 -70 2]);

[Sam Chak]

@koorosh dastan. yes, the cost function should return only one scalar value. Before solving any optimization problem, I typically analyze and test my designed cost function to ensure it operates as expected. A simple example using a Bivariate Quadratic Function is provided below.

%% Test 1: Bivariate Quadratic Function
x = ones(1, 2)  % supply 2 values to the Cost function

x = 1×2

1 1

J = myCost(x)   % returns one scalar value as expected

J = 0

%% Test 2: Dastan 64-variable Cost function
x = ones(1, 64) % supply 64 values to the Cost function

x = 1×64

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

J = costy(x)    % cannot return one scalar value

Index exceeds the number of array elements. Index must not exceed 64.

Error in solution>costy (line 42)
g(h,aa) = g(h,aa)+(x(h) * ( exp(j*(h-1) * (k*d*sind(teta1(aa)+(ww*x(h+elementNumb))))))); %w W

%% My 2-variable Cost function
function J = myCost(x)
    J = (x(1) - 1)^2 + (x(2) - 1)^2;    % Bivariate Quadratic Function
end

%% Dastan 64-variable Cost 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    = 0.67*l;           %Distant of each element
    elementNumb = 34;
    step = 0.5;
    
    teta1 = -70:step:-40;   % θ1 range
    teta2 = -40:step:6;     % θ2 range
    teta3 =  11:step:15;    % θ3 range
    teta4 =  18:step:45;    % θ4 range
    teta5 =  45:step:60;    % θ5 range
    
    tetat          = [teta1, teta2, teta3, teta4, teta5];
    lenteta1       = length(teta1);
    sumLenteta12   = length(teta1) + length(teta2);
    sumLenteta123  = length(teta3) + sumLenteta12;
    sumLenteta1234 = sumLenteta123 + length(teta4);
    
    g  = zeros(elementNumb, length(tetat));
    ww = 90;
        for h = 1:elementNumb    
            %%teta1
            for aa = 1:length(teta1)
                g(h,aa) = g(h,aa)+(x(h) * ( exp(j*(h-1) * (k*d*sind(teta1(aa)+(ww*x(h+elementNumb)))))));      %w W
            end
            %%teta2
            for bb=(lenteta1+1):(sumLenteta12)
                g(h,bb) = g(h,bb)+( x(h) * exp(j*(h-1) * (k*d*sind(teta2(bb-lenteta1)+(ww*x(h+elementNumb)))))); %with W
            end    
            %%teta3
            for cc = (sumLenteta12+1):(length(teta3)+sumLenteta12)
                g(h,cc) = g(h,cc)+ (x(h) * exp(j*(h-1) * (k*d*sind(teta3(cc-sumLenteta12) +(ww*x(h+elementNumb))))));  %w W
            end    
            %%teta4    
            for dd = (sumLenteta123+1):(sumLenteta123+length(teta4))
                g(h,dd) = g(h,dd)+( x(h) * exp(j*(h-1) * (k*d*sind(teta4(dd-(sumLenteta123)) + (ww*x(h+elementNumb))))));  %w W           
            end
            %%teta5
            for ee = (sumLenteta1234+1):(sumLenteta1234+length(teta5))
                g(h,ee) = g(h,ee)+( x(h) * exp(j*(h-1) * (k*d*sind(teta5(ee-(sumLenteta1234)) + (ww*x(h+elementNumb))))));  %w W
            end
            % disp([x(1),x(2),x(3),x(35),x(36),x(50)]);
        end
    w1 = 0;
    w2 = 0;
    w3 = 0;
    w4 = 0;
    w5 = 0;
    
    b = abs(sum(g));
    % b=b/max(b);
    % b=20*log10(abs(b));
    %% for each point evaluate    
    % b = [b(1:lenteta1)+w1,b(lenteta1+1:sumLenteta12)+w2,(1./b(sumLenteta12+1:sumLenteta123))+w3 ... 
    %     ,b(sumLenteta123+1:sumLenteta1234)+w4,b(sumLenteta1234+1:length(tetat))+w5];
    % y = b;
    
    %% for one point evaluate
    b1   =  max(b(1:lenteta1))+w1;
    b2   =  max(b(lenteta1+1:sumLenteta12))+w2;
    b3   = -max(b(sumLenteta12+1:sumLenteta123))+w3 ; 
    b4   =  max(b(sumLenteta123+1:sumLenteta1234))+w4;
    b5   =  max(b(sumLenteta1234+1:length(tetat)))+w5;
    totb = b1 + b2 + b3 + b4 + b5;
    y    = totb;
end