Optimization/ Error minimization to reach target

Hello

I have a problem where in I calculate Ratio_final which is a column vector. I also have column vector Ratio_target which is my target values. I basically need to minimize the error between Ratio_final and Ratio_target to as close as possible(maybe tolerance of 0.1 %). The parameter to vary would be the values in Ratio_one, Ratio_two and Ratio_three which have to be within certain limits (the limits I ll define later)

But the problem is that each value in Ratio_final are somehow interdependent on each other based on the calculation done to achieve its value if you look at the Matlab code that I have appended. Please let me know how to proceed with the next step to achieve the solution.

P.S- I do not have any toolbox to work with as of now.

            % e12 e13 e14 e15 e23 e24 e25 e34 e35 e45
Gear_pattern=[ 0   0   0   0   0   1   0   0   0   1;
               0   0   1   0   0   0   0   0   0   1;
               0   0   0   0   0   2   0   0   0   1;
               0   0   0   1   0   0   0   0   0   0;
               0   0   0   0   0   1   0   0   0   2;
               0   0   1   0   0   0   0   0   0   2;
               0   0   0   0   0   2   0   0   0   2;
               0   0   0   2   0   0   0   0   0   0;
               0   0   0   0   0   1   0   0   0   3;
               0   0   1   0   0   0   0   0   0   3;
               0   0   0   0   0   2   0   0   0   3];

          % x12  x13     x14     x15    x23     x24   x25  x34  x35     x45
Ratio_one=  [0;   0;   1.274;   7.054;   0;   1.623;   0;   0;   0;    8.99];
Ratio_two=  [0;   0;       0;   2.674;   0;       1;   0;   0;   0;   3.408];
Ratio_three=[0;   0;       0;       0;   0;       0;   0;   0;   0;   1.292];

Ratio_matrix=zeros(size(Gear_pattern));
Ratio_matrix=zeros(size(Gear_pattern));
for i=1:size(Gear_pattern,1)

    for j=1:size(Gear_pattern,2)

        if Gear_pattern(i,j)==1

        Ratio_matrix(i,j)=Ratio_one(j);

        elseif Gear_pattern(i,j)==2
                Ratio_matrix(i,j)=Ratio_two(j);

        elseif Gear_pattern(i,j)==3
                Ratio_matrix(i,j)=Ratio_three(j);
        else
        end

    end

end

Ratio_final=size(Ratio_matrix,2);

for u=1:size(Ratio_matrix,1)

    prod=1;

    for v=1:size(Ratio_matrix,2)

        if Ratio_matrix(u,v)>0
            temp=Ratio_matrix(u,v);
            prod_temp=temp*prod;
            prod=prod_temp;

        else
        end

    end
    Ratio_final(u,1)=prod;

end
Ratio_target=[15;12;9;8;6;5;4;3;3;2;2];