fmincon constraints error: Aeq must have 81 column(s).

I am trying to minimize the norm of a matrix. But I want to put constraints on my argument x which is a 9x9 matrix such that x*ones(9,1) = ones(9,1) i.e all the rows of matrix x must sum to one

fun = @(x) norm(A*x - B);
rng(4)
x0 = rand(9,9);
lb = zeros(1,81);
ub = ones(1,81)*0.999999;
A = [];
b = [];
Aeq = ones(9,1);
beq = ones(9,1);
nonlcon = [];
options = optimoptions(@fmincon,'Algorithm','sqp','MaxFunctionEvaluations',5000)
x = fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon, options);

Here A and B are two 15x9 matrices.

I get this error: Aeq must have 81 column(s).

[Ameer Hamza]

What are the values of A and B in

fun = @(x) norm(A*x - B);

[AMIT PAWAR]

A =  [0.0020    0.0061    0.0095    0.0155    0.0141    0.0252    0.0321    0.0257    0.0102;
    0.0067    0.0087    0.0023    0.0079    0.0058    0.0142    0.0334    0.0214    0.0202;
    0.0029    0.0049    0.0000    0.0039    0.0148    0.0126    0.0345    0.0167    0.0174;
    0.0000    0.0015    0.0027    0.0033    0.0234    0.0133    0.0286    0.0139    0.0137;
    0.0000    0.0005    0.0094    0.0055    0.0243    0.0140    0.0216    0.0123    0.0110;
    0.0012    0.0019    0.0121    0.0087    0.0212    0.0140    0.0165    0.0112    0.0093;
    0.0029    0.0046    0.0123    0.0111    0.0176    0.0134    0.0133    0.0104    0.0079;
    0.0042    0.0074    0.0118    0.0125    0.0146    0.0126    0.0112    0.0096    0.0055;
    0.0054    0.0101    0.0109    0.0131    0.0121    0.0118    0.0096    0.0090    0.0000;
    0.0055    0.0127    0.0103    0.0139    0.0096    0.0111    0.0074    0.0084    0.0000;
    0.0035    0.0141    0.0120    0.0155    0.0062    0.0107    0.0026    0.0077    0.0000;
    0.0010    0.0109    0.0186    0.0192    0.0014    0.0106    0.0000    0.0064    0.0000;
    0.0001    0.0043    0.0231    0.0245    0.0000    0.0108    0.0000    0.0041    0.0296;
    0.0000    0.0008    0.0137    0.0260    0.0000    0.0110    0.0000    0.0041    0.0885;
    0.0000    0.0001    0.0038    0.0164    0.0047    0.0102    0.0000    0.0088    0.0600;
    0.0000    0.0000    0.0009    0.0060    0.0059    0.0086    0.0000    0.0142    0.0375]

B = [0.0067    0.0087    0.0023    0.0079    0.0058    0.0142    0.0334    0.0214    0.0202;
    0.0029    0.0049    0.0000    0.0039    0.0148    0.0126    0.0345    0.0167    0.0174;
    0.0000    0.0015    0.0027    0.0033    0.0234    0.0133    0.0286    0.0139    0.0137;
    0.0000    0.0005    0.0094    0.0055    0.0243    0.0140    0.0216    0.0123    0.0110;
    0.0012    0.0019    0.0121    0.0087    0.0212    0.0140    0.0165    0.0112    0.0093;
    0.0029    0.0046    0.0123    0.0111    0.0176    0.0134    0.0133    0.0104    0.0079;
    0.0042    0.0074    0.0118    0.0125    0.0146    0.0126    0.0112    0.0096    0.0055;
    0.0054    0.0101    0.0109    0.0131    0.0121    0.0118    0.0096    0.0090    0.0000;
    0.0055    0.0127    0.0103    0.0139    0.0096    0.0111    0.0074    0.0084    0.0000;
    0.0035    0.0141    0.0120    0.0155    0.0062    0.0107    0.0026    0.0077    0.0000;
    0.0010    0.0109    0.0186    0.0192    0.0014    0.0106    0.0000    0.0064    0.0000;
    0.0001    0.0043    0.0231    0.0245    0.0000    0.0108    0.0000    0.0041    0.0296;
    0.0000    0.0008    0.0137    0.0260    0.0000    0.0110    0.0000    0.0041    0.0885;
    0.0000    0.0001    0.0038    0.0164    0.0047    0.0102    0.0000    0.0088    0.0600;
    0.0000    0.0000    0.0009    0.0060    0.0059    0.0086    0.0000    0.0142    0.0375;
    0.0000    0.0000    0.0003    0.0021    0.0041    0.0073    0.0085    0.0167    0.0286]

copy and paste this into your script.

Answer 1

[Ameer Hamza]

See this example. This consider random values for matrices A and B in fun

rng(0);
A = rand(9);
B = rand(9);

fun = @(x) norm(A*reshape(x,9,9) - B);
rng(4)
x0 = rand(1,81);
lb = zeros(1,81);
ub = ones(1,81)*0.999999;
A = [];
b = [];
Aeq = repelem(eye(9),1,9);
beq = ones(9,1);
nonlcon = [];
options = optimoptions(@fmincon,'Algorithm','sqp','MaxFunctionEvaluations',5000);
x = fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon, options);

x = reshape(x, 9, 9);

[AMIT PAWAR]

Thanks Ameer...it works

[Ameer Hamza]

Glad to be of help.