Function optimization meeting conditions

Question

Jon Bilbao 2023-6-7

0
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https://ww2.mathworks.cn/matlabcentral/answers/1979774-function-optimization-meeting-conditions

评论： Jon Bilbao 2023-6-8

How can i optimize the I function, i want to find the values of h(j) that minimize I, meetentig the conditions h(j+1)>h(j), h(end)<120 and h(j+1)-h(j)<1.25 ?

ht is a array beiing its size ht(lt,lc) or the same ht(i,j) and it is calculated in another function. The formula of Ins is Ins=ht(i,j)-h(j).

Thanks for the help

function [h] = hp(ht, Lc, Lt)
lt = 0:0.5:Lt;
lc = 0:0.5:Lc;
Ins = cell(length(lt), length(lc));
h= cell(length(Lc));
for i = 1:length(lt)
    for j = 1:length(lc)
        Ins{i,j} = @(h) (ht(i,j) - h);
    end
end
h0 = zeros(size(lc)); 
A = [];
b = [];
Aeq = [];
beq = [];
lb = [];
ub = [];
nonlcon = @constraints;
h = fmincon(@(h) Ins, h0, A, b, Aeq, beq, lb, ub, nonlcon);
end
function [c] = constraints(h)
    c>0;
    c = h(2:end) - h(1:end-1); 
   end

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Jon Bilbao 2023-6-7

在 MATLAB Online 中打开

I'm going to try to explain myself better. In the problem I want to solve, I have a matrix ht(i,j), which means there is a value ht for each i,j. What I need is the value h(j), which does not depend on i. This value should minimize the differences with all the ht values in "i", and I need to repeat this for each j. Therefore, the difference Ins is not a single value; there will be as many differences as ht values. My objective is not to make the differences between ht and h equal to 0; rather, I want to find the h that minimizes the maximum value of Ins across all "i". For example, if I have a matrix ht with the following rows (7,8) and (5,9), I need to find h(1) such that the maximum value between 7-h(1) and 8-h(1) is minimized, and h(2) such that the maximum value between 5-h(2) and 9-h(2) is minimized, with the additional condition that h(2) > h(1). Currently, the function I have is as follows:

unction [h] = hp3(ht, Lc)
lc = 0:0.5:Lc;
Ins = @(h) ht - h;
h = zeros(size(lc));
h0 = zeros(size(lc)); 
A = [];
b = [];
Aeq = [];
beq = [];
lb = [];
ub = inf(size(h));
ub(end) = h(end);
h = fmincon(Ins, h0, A, b, Aeq, beq, lb, ub, @constraints);
end
function [c, ceq] = constraints(h)
    c = h(2:end) - h(1:end-1);
    ceq = [];
end

Torsten 2023-6-8

编辑：Torsten 2023-6-8

在 MATLAB Online 中打开

If ht is nxm, the linear constraints can be defined by A and b as in the code below.

A and b are then used in the call to the optimizer, e.g.

h = fmincon(fun,h0,A,b)

Now it's your turn to define the objective function and the call to "fmincon" (or some similar optimizer).

(And incidentally the .^2 appears for the summands in the objective :-) )

m = 4;
v1 = ones(m,1);
w1 = -ones(m-1,1);
A1 = diag(v1) + diag(w1,1)
A1 = 4×4
     1    -1     0     0
     0     1    -1     0
     0     0     1    -1
     0     0     0     1
b1 = [zeros(m-1,1);120];
v2 = -ones(m,1);
w2 = ones(m-1,1);
A2 = diag(v2) + diag(w2,1);
A2(end,:) = []
A2 = 3×4
    -1     1     0     0
     0    -1     1     0
     0     0    -1     1
b2 = 1.25*ones(m-1,1);
A = [A1;A2]
A = 7×4
     1    -1     0     0
     0     1    -1     0
     0     0     1    -1
     0     0     0     1
    -1     1     0     0
     0    -1     1     0
     0     0    -1     1
b = [b1;b2]
b = 7×1
         0
         0
         0
  120.0000
    1.2500
    1.2500
    1.2500

Jon Bilbao 2023-6-8

在 MATLAB Online 中打开

it cant be solved like thah because ht is too big, ht is a 401x51 matrix

Error using fmincon

A must have 2601 column(s).

Error in hpp (line 22)

h = fmincon(I,h0,A,b);

function [h] = hpp(ht)
[n,m]=size(ht);
I=@(h) (ht-h);
h0=zeros(m);
v1 = ones(m,1);
w1 = -ones(m-1,1);
A1 = diag(v1) + diag(w1,1);
b1 = [zeros(m-1,1);120];
v2 = -ones(m,1);
w2 = ones(m-1,1);
A2 = diag(v2) + diag(w2,1);
A2(end,:) = [];
b2 = 1.25*ones(m-1,1);
A = [A1;A2];
b = [b1;b2];
h = fmincon(I,h0,A,b);
end

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Answer 1

Torsten 2023-6-8

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1979774-function-optimization-meeting-conditions#answer_1252729

移动：Torsten 2023-6-8

在 MATLAB Online 中打开

ht = rand(401,51);
[n,m]=size(ht);
I=@(h) sum(sum((ht-h).^2));
h0 = zeros(1,m);
v1 = ones(m,1);
w1 = -ones(m-1,1);
A1 = diag(v1) + diag(w1,1);
b1 = [zeros(m-1,1);120];
v2 = -ones(m,1);
w2 = ones(m-1,1);
A2 = diag(v2) + diag(w2,1);
A2(end,:) = [];
b2 = 1.25*ones(m-1,1);
A = [A1;A2];
b = [b1;b2];
[h,fval,exitflag] = fmincon(I,h0,A,b)
Local minimum possible. Constraints satisfied.

fmincon stopped because the size of the current step is less than
the value of the step size tolerance and constraints are 
satisfied to within the value of the constraint tolerance.
h = 1×51
    0.4889    0.5003    0.5003    0.5003    0.5003    0.5042    0.5042    0.5042    0.5042    0.5042    0.5042    0.5042    0.5042    0.5042    0.5042    0.5042    0.5042    0.5042    0.5042    0.5042    0.5042    0.5042    0.5042    0.5042    0.5042    0.5042    0.5042    0.5042    0.5042    0.5042
fval = 1.7157e+03
exitflag = 2

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Jon Bilbao 2023-6-8

That works, thank you so much.

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Answer 2

rakshit gupta 2023-6-7

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1979774-function-optimization-meeting-conditions#answer_1252084

在 MATLAB Online 中打开

You can consider following changes to the code to optimize the function while meeting the condition h(j+1)>h(j).

Modify the Ins cell array to a function handle that takes in the h array.

Ins = @(h) ht - h;

2. Modify the h array to a vector instead of a cell array.

h = zeros(size(lc));

3. Add the upper bound constraint to ensure h(j+1) > h(j).

ub = inf(size(h));
ub(end) = h(end);

4. Modify the constraints function to return the inequality constraint.

function [c, ceq] = constraints(h)
    c = h(2:end) - h(1:end-1);
    ceq = [];
end

5. Call the fmincon function with the changes made above.

h = fmincon(Ins, h, A, b, Aeq, beq, lb, ub, @constraints);

These changes could help in optimizing the function.

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rakshit gupta 2023-6-8

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Yes, you can try modifying 'h' vector by changing the creation of the 'h' vector to use the same size and data type as 'ht',

h = zeros(size(ht), 'like', ht);

This may help in making Ins scalar.

Jon Bilbao 2023-6-8

But h its not of the same size as ht

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