Facing error in the optimization part. Kindly suggest solution

clc;
clear;
a=[241.0, 301.0, 261.0, 221.0, 281.0, 361.0, 401.0, 361.0, 301.0, 321.0, 221.0, 281.0, 201.0, 201.0, 261.0, 141.0, 181.0, 201.0, 161.0, 121.0, 161.0, 221.0, 141.0, 161.0, 201.0, 221.0, 221.0, 201.0, 221.0, 221.0, 241.0, 301.0, 281.0, 221.0];
b=[130.0, 150.0, 190.0, 170.0, 210.0, 130.0, 170.0, 230.0, 210.0, 190.0, 230.0, 270.0, 290.0, 330.0, 330.0, 150.0, 130.0, 150.0, 150.0, 170.0, 190.0, 210.0, 230.0, 230.0, 70.0, 90.0, 110.0, 110.0, 130.0, 50.0, 110.0, 110.0, 70.0, 70.0];

lb_w=[1e-04, 1e-04, 1e-04,1e-04, 1e-04, 1e-04,1e-04];
ub_w=[10000,10000,10000,10000,10000,10000,10000];
reg1=[11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11];
reg2=[10,10,10,10,10,11,11,11,11,11,12,12,12,12,12,17,17,17,17,18,18,18,18,18,38,38,38,38,38,39,39,39,39,39];
lb_x=[283.6939,203.9050,179.9683,134.7546,100.1794, 177.3087,207.4512];
ub_x=[419.3351  313.8364  296.1055  210.9974  231.3879  242.9129  325.3615];
lb_y=[123.6309  109.4000  209.0163  122.7415  153.8715   53.3659   19.5675];
ub_y=[259.7138  215.2423  360.2195  165.4341  240.1463  144.0878  138.7512];

initial_x = zeros(1, 7);
initial_y = zeros(1, 7);
initial_w = zeros(1, 7);
disp(['initial_x: ', num2str(initial_x)])

initial_x: 0  0  0  0  0  0  0

% Concatenating initial guesses, lower bounds, and upper bounds
%initialVars = [initial_x, initial_y, initial_w];
initialVars = [lb_x, lb_y, lb_w];
lb = [lb_x, lb_y, lb_w];
ub = [ub_x, ub_y, ub_w];
disp(lb);

  Columns 1 through 19

  283.6939  203.9050  179.9683  134.7546  100.1794  177.3087  207.4512  123.6309  109.4000  209.0163  122.7415  153.8715   53.3659   19.5675    0.0001    0.0001    0.0001    0.0001    0.0001

  Columns 20 through 21

    0.0001    0.0001

disp(ub);

   1.0e+04 *

  Columns 1 through 19

    0.0419    0.0314    0.0296    0.0211    0.0231    0.0243    0.0325    0.0260    0.0215    0.0360    0.0165    0.0240    0.0144    0.0139    1.0000    1.0000    1.0000    1.0000    1.0000

  Columns 20 through 21

    1.0000    1.0000

% Optimization options
options = optimoptions('fmincon', 'Display', 'iter', 'Algorithm',   'interior-point');
% Defining the objective function
objFun = @(vars) objective(vars, a, b, reg1, reg2);
% Run optimization
[optimalVars, fval] = fmincon(objFun, initialVars, [], [], [], [], lb, ub, [], options);

Initial point X0 is not between bounds LB and UB; 
FMINCON shifted X0 to strictly satisfy the bounds.

Index exceeds the number of array elements. Index must not exceed 7.

Error in solution>objective (line 59)
p(i)=((x(r1)-a(i))^2 + (y(r1)-b(i))^2)-abs(w(r1));

Error in solution>@(vars)objective(vars,a,b,reg1,reg2) (line 29)
objFun = @(vars) objective(vars, a, b, reg1, reg2);

Error in fmincon (line 563)
initVals.f = feval(funfcn{3},X,varargin{:});

Caused by:
Failure in initial objective function evaluation. FMINCON cannot continue.

% Extract optimal x, y, and w
optimal_x = optimalVars(1:7);
optimal_y = optimalVars(8:14);
optimal_w = optimalVars(15:end);
% Display results
disp('Optimal x:');
disp(optimal_x);
disp('Optimal y:');
disp(optimal_y);
disp('Optimal w:');
disp(optimal_w);
disp('Objective function value:');
disp(fval);
hold on
scatter(a,b,"blue","filled")
scatter(optimal_x, optimal_y, '*','red');
grid on;
hold off
% Objective function
function f = objective(vars, a, b, reg1, reg2)
x = vars(1:7);
y = vars(8:14);
w = vars(15:end);
f = 0;
for i = 1:a(1:5)
    r1=reg1(i);
    
    p(i)=((x(r1)-a(i))^2 + (y(r1)-b(i))^2)-abs(w(r1));
    for j=1:a(6:34)
        r2 = reg2(j);
        q(j)=((x(r2)-a(j))^2 + (y(r2)-b(j))^2)-abs(w(r2));
        f = f + p(i)-q(j);
    end
end
end

error: Index exceeds the number of array elements. Index must not exceed 7.

Error in grid_weight>objective (line 106)

p(i)=((x(r1)-a(i))^2 + (y(r1)-b(i))^2)-abs(w(r1));

Error in grid_weight>@(vars)objective(vars,a,b,reg1,reg2) (line 71)

objFun = @(vars) objective(vars, a, b, reg1, reg2);

Error in fmincon (line 568)

initVals.f = feval(funfcn{3},X,varargin{:});

Error in grid_weight (line 74)

[optimalVars, fval] = fmincon(objFun, initialVars, [], [], [], [], lb, ub, [], options);

Answer 1

[Cris LaPierre]

You have an indexing issue. Namely, w(r1).

• r1=reg1(i)
• reg1(1) = 11
• w only has 7 elements

reg1=[11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11];
w = [1e-04, 1e-04, 1e-04,1e-04, 1e-04, 1e-04,1e-04]

w = 1×7

1.0e-04 * 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

r1 = reg1(1)

r1 = 11

w(r1)

Index exceeds the number of array elements. Index must not exceed 7.

You need to adjust your code so that your index does not exceed the length of your vector.

[Cris LaPierre]

Also note that the following line of code is likely not doing what you think it is doing

for i = 1:a(1:5)

The end result will be the same as if you had written for i = 1:a(1)