why fminimax lost the point i want to optimize but patternsearch doesnt?

i want to use fminimax because i like to have quantize variable so i like to use it but it try to optimize another point(zero) i think cost func should be correct because patternsearch work almost correct

this is cost func i want to implement

% close all
clear all
t0 = tic();
elementNumb=32;

%%%%%%%%%%%
num_iterations = 1; % Adjust this as needed
% 
for iteratt = 1:num_iterations
%% Generate random values for w1, w2, w3, w4, w5 within the specified range
global w
    w=ones(1,32);
    w(1:10) = randi([1, 10]) * rand(1);
    w(11:18) = randi([1, 10]) * rand(1);
    w(19) = randi([1, 10]) * rand(1);
    w(20) = randi([1, 10]) * rand(1);
    w(21) = randi([1, 10]) * rand(1);
    w(22) = randi([1, 10]) * rand(1);
    w(23) = randi([1, 10]) * rand(1);
    w(24) = randi([1, 10]) * rand(1);
    w(25:32) = randi([1, 10]) * rand(1);

   % Set the random values as weights
    w_values = w;
%%%%%%%%%%%%
%%
random_numbersw = ones(1,elementNumb);
ubb=1;
lbb=-1;
random_numberst =-0.23889*(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



%% Algoritm
%% PSO
hybridopts = optimoptions('patternsearch','Display', 'iter','MaxIterations',1e5);
options = optimoptions('particleswarm','SwarmSize',150,'HybridFcn',{'patternsearch',hybridopts},...
    'Display', 'iter','InitialSwarmMatrix' , x0,'MaxIterations',1e5);
x = particleswarm(@costy,length(x0),lb,ub,options); 
%%

%% fminimax
%  options = optimoptions(@fminimax,'FunctionTolerance',1e-12,	...
%     'MaxIterations',9e3,'OptimalityTolerance',1e-40,'MaxFunctionEvaluations',2e5 ); 
% [x,fval,maxfval,exitflag,output,lambda] = fminimax(@costy,x0,[],[],[],[],lb,ub,[],options);
% 
%%





output_filename = sprintf('output_data_iteration%d.mat', iteratt);
% save(output_filename, 'x', 'fval', 'maxfval', 'exitflag', 'output', 'lambda', 'w_values');
save(output_filename, 'x', 'w_values');



    %%after optimize finish get me result
    elementNumb=32;
    deltaTeta=x(1:elementNumb*2);
    f=9.5*10^9;
    j=sqrt(-1);
    l=(3*10^8)/f;
    k=(2*pi)/l;
    d=0.7*l;
    teta=((-1*87.6):0.1:(1*84));
    y=0;
    % for h=1:elementNumb
    %     y=y+deltaTeta(h)*exp(j*(h-1)*(k*d*sind(teta+180*deltaTeta(h+elementNumb))));
    % end
g = zeros(elementNumb, length(teta));
for h=1:elementNumb
        for iteta=1:length(teta)
        g(h,iteta)=g(h,iteta)+deltaTeta(h)*exp(j*(h-1)*(k*d*sind(teta(iteta)+180*deltaTeta(h+elementNumb))));
        end
 end
bb = abs(sum(g));

figure;
% 
plot(teta,20*log10(abs(bb)),'k')
% 
axis([-100 100 -60 40]);
end
dt = toc(t0);
beep;
beep;
%% my main function
function y = costy(x)
global w;
freq = 9.5*(10^9);       %Freq
j = sqrt(-1);        %Define Imaginary
l =(3*(10^8))/freq;    %Lambda
k = (2*pi)/l;        %Constant
d = 0.7*l;           %Distant of each element
elementNumb = 32;
step = 0.1;
% teta=((-1*87.6):step:(1*85));
teta=((-1*36.2):step:(1*72.4));
ww=180;
g = zeros(elementNumb, length(teta));
    for h=1:elementNumb
        for iteta=1:length(teta)
        g(h,iteta)=g(h,iteta)+x(h)*exp(j*(h-1)*(k*d*sind(teta(iteta)+ww*x(h+elementNumb))));
        end
    end
bb = abs(sum(g));
[bbmax,bddmax]=max(bb);
bb=bb/(bbmax);
bb=20*log10(abs(bb));

% t= [ -87.6000000000000	-83.5000000000000	-79	-73.8000000000000	-67.4000000000000	-57.8000000000000	-36.2000000000000	-26.6000000000000	-20.2000000000000	-15	-10.5000000000000	-6.40000000000001	-2.59999999999999	1	4.30000000000000	7.50000000000000	10.6000000000000	13.6000000000000	16.5000000000000	19.3000000000000	22.1000000000000	24.8000000000000	27.5000000000000	30.1000000000000	32.7000000000000	35.3000000000000	37.9000000000000	40.4000000000000	45.6000000000000	48.1000000000000	50.7000000000000	53.3000000000000	55.9000000000000	58.5000000000000	61.2000000000000	63.9000000000000	66.7000000000000	69.5000000000000	72.4000000000000	75.4000000000000	78.5000000000000	81.7000000000000	85];
t= [ 	-36.2000000000000	-26.6000000000000	-20.2000000000000	-15	-10.5000000000000	-6.40000000000001	-2.59999999999999	1	4.30000000000000	7.50000000000000	10.6000000000000	13.6000000000000	16.5000000000000	19.3000000000000	22.1000000000000	24.8000000000000	27.5000000000000	30.1000000000000	32.7000000000000	35.3000000000000	37.9000000000000	40.4000000000000	45.6000000000000	48.1000000000000	50.7000000000000	53.3000000000000	55.9000000000000	58.5000000000000	61.2000000000000	63.9000000000000	66.7000000000000	69.5000000000000	72.4000000000000	];

%i dont know ehy it happens but when my function is zero it shoul change
%the x 
for opi=1:length(t)
    if t(opi)<0.001 && t(opi)>-0.001
      t(opi)=0;
    end
end
% Initialize a counter
tCount = length(t);

% length of each interval
lentt = cell(1, tCount-1);
for iou = 1:tCount-1
    if iou == 1
        lentt{iou} =length( t(iou) : step : t(iou + 1));
    else
        lentt{iou} = length(t(iou)+ step : step : t(iou + 1));
    end
end
lentt{13}=lentt{13}+1;
lentt{17}=lentt{17}+1;
% value of each inervals get lable

for uiu=1:tCount-1
    if uiu==1
    lenttt(uiu)=(lentt{uiu});
    else
    lenttt(uiu)=lenttt(uiu-1)+lentt{uiu};  
    end
end
% Different intervals for optimization
cv = cell(1, tCount-1);    %there are cv for each bb
for jjj=1:tCount-1
    if jjj==1
    cv{jjj} = bb(1:(lenttt(jjj)))*1;
    else 
    cv{jjj} = bb(lenttt(jjj-1)+1:(lenttt(jjj)))*1;
    end
end

sll=[-28.7693818430320	-29.2269260908810	-29.5817391344837	-29.8386379476817	-30.0092809774479	-30.0986002759175	-30.0933861813434	-30.0130434044565	-29.8472703208587	-29.5796408403258	-29.2280789837052	-28.7750639926713	-28.2010451569390	-27.4986515399832	-26.6454094872800	-25.6022425933528	-24.3178386609530	-22.7110953803777	-20.6212057739930	-17.7459944773407	-13.2421565888999	0	-13.2421565888999	-17.7459944773407	-20.6212057739930	-22.7110953803777	-24.3178386609530	-25.6022425933529	-26.6454094872800	-27.4986515399832	-28.2010451569390	-28.7750639926713		];
sll(1:9)=sll(1:9)+1;
sll(10:18)=sll(10:18)-3;
sll(19:21)=sll(19:21)-2;
sll(22:25)=sll(22:25)-1;
sll(26:29)=sll(26:29)-2;
sll(30:32)=sll(30:32)-2;

sll(22)=0;
%                                         %%%Keng Algorithm
maximo=22;
steppyup=2;
steppydown=2;
D1 = 0 ;
D2 = 0;
D3 = 0;
for lll=1:tCount-1
    bt=cv{lll};

%% this function is main fuction which i used in another file
       if lll==maximo
             for ppp=(1+steppydown):(length(bt)-steppyup) 
              if sll(lll)>bt(ppp)   %decrease max
              D2 = D2 + sll(lll) - bt(ppp); 
              end
             end
             D2=w(lll)*D2;
        else
        for ppp=1:length(bt)
          if bt(ppp)>sll(lll)
            D1 = D1 + bt(ppp)-sll(lll);
          end
        end  
        D3=w(lll)*D1+D3;
        D1=0;
        end
end

a1 = 1; %0.4;
a2 = 1;  %0.3;
a3 = 1; % 0.4;
y=a1*D3+a2*D2;



%%
end

Answer 1

[Ronit]

Hello Koorosh,

There could be several reasons why you are encountering issues while using the "fminimax" function for optimization such as the setup of the cost function, initial conditions, or constraints.

I would suggest you to adjust the options for "fminimax". You may need to experiment with parameters like "MaxIterations", "FunctionTolerance" , and "OptimalityTolerance". Sometimes, more iterations or a different tolerance can lead to better results.

options = optimoptions('fminimax', ...
    'Display', 'iter', ...
    'FunctionTolerance', 1e-6, ...
    'MaxIterations', 1000, ...
    'OptimalityTolerance', 1e-6, ...
    'MaxFunctionEvaluations', 5000);

Utilizing a code similar to the one mentioned above may assist in achieving better results. In this manner, "fminimax" is able to locate a point locally that satisfies the constraints.

I hope it helps with your query!