Optimization to minimize output

Hello,

I am trying to optimize the lengths to minimize the power ( details in the code)

I am unable to proceed with the optimization part. ( Iam not getting the expected result of optimized power)

Any help would be greatly appreciated.

% Objective:Optimize the lengths to minimze the power using a new variable.

%Constants
k= 1;
w=1;

%Variable lengths
l1 = 3*(5)^0.5;
l2 = 5*(2)^0.5

l2 = 7.0711

l3 = sqrt(5);


v1 = sqrt(5);
v2 = 2*sqrt(2);
v3 = 2*sqrt(5);



% Expressing the l and v in terms of a b and c. Open to expressing differently
% if it helps the objective below.
a = l1*v1;
b = l2*v2;
c = l3*v3;

%Actual Power
 P = (l1*v1 + l2*v2 + l3*v3)*k*w; % Power

% Objective
%To search and find the values for a, b and c to minimize power

%Considering x to represent a,b and c.

fun = @(x)(x(:,1) + x(:,2) + x(:,3)).*k.*w;

[X1, X2, X3] = ndgrid(0:.1:2); % Should I give this condition in a nested loop?

X = [X1(:), X2(:), X3(:)];

P = fun(X);
[bestP, idx] = min(P(:))

bestP = 0

idx = 1

best_X = X(idx,:)

best_X = 1×3

0 0 0

[Matt J]

Your post now contains the results of running the code (I took the liberty...). The answer looks correct to me.

Answer 1

[Walter Roberson]

% Objective:Optimize the lengths to minimze the power using a new variable.

%Constants
k= 1;
w=1;

%Variable lengths
l1 = 3*(5)^0.5;
l2 = 5*(2)^0.5

l2 = 7.0711

l3 = sqrt(5);


v1 = sqrt(5);
v2 = 2*sqrt(2);
v3 = 2*sqrt(5);



% Expressing the l and v in terms of a b and c. Open to expressing differently
% if it helps the objective below.
a = l1*v1;
b = l2*v2;
c = l3*v3;

%Actual Power
 P = (l1*v1 + l2*v2 + l3*v3)*k*w; % Power

% Objective
%To search and find the values for a, b and c to minimize power

%Considering x to represent a,b and c.

fun = @(x)(x(:,1) + x(:,2) + x(:,3)).*k.*w;

[X1, X2, X3] = ndgrid(0:.1:2); % Should I give this condition in a nested loop?

X = [X1(:), X2(:), X3(:)];

P = fun(X);
[bestP, idx] = min(P(:))

bestP = 0

idx = 1

best_X = X(idx,:)

best_X = 1×3

0 0 0

This is obviously the correct output for the formula.

k is positive. w is positive. k*w is positive. k*w is being multiplied by (x1 + x2 + x3)

To get the smallest result of a multiplication of a positive number and another number, you want the second number to be as small as possible.

Your x1, x2, x3 are all bounded by 0 below. Increasing x1 or x2 or x3 would increase the sum x1+x2+x3 . So the smallest x1+x2+x3 is at the lower bound, where x1 = x2 = x3 = 0.

So your minima is clearly at x1 = x2 = x3 = 0 with power 0 .

[Anand Ra]

@Matt J@Walter Roberson

Really sorry. I failed to recognize the obvious earlier. Below is what I wanted to optimize ( a,b,c,d and e) to obtain the minimum power

% Objective:Optimize the lengths to minimze the power using a new variable.

%Constants

k= 2;

w=1;

%Variables

AB = sqrt(a^2 + b^2);

BC = sqrt( c^2 + ((e-d)/2)^2 );

CS = sqrt( c^2 + ((e-d)/2)^2 );

VAB = sqrt(((a*v)^2/((4*b*b)) + (v^2)/2 ));

% VBS = sqrt(((a*v)^2/((4*b*b)) + (v^2)/2 ));

VCS = ((2*c)/(e-d))*sqrt(AB^2);

VBC= CS^2 + BS^2;

%Actual Power

%P = (AB*VAB + BC*VBC + CS*VCS)*k*w; % Power

%

% Objective

%To search and find the values for a, b, c d and eto minimize power

%%% Not sure how to write the function for above%%%%

%Attempt

fun = @(x)(x(:,1) + x(:,2) + x(:,3) + x(:4) + x(5).*k.*w;

[X1, X2, X3, X4, X5] = ndgrid(0:.1:2); % Should I give this condition in a nested loop?

X = [X1(:), X2(:), X3(:), X4(:), X5(:)];

P = fun(X);

[bestP, idx] = min(P(:))

best_X = X(idx,:)

[Walter Roberson]

fun = @(x)(x(:,1) + x(:,2) + x(:,3) + x(:4) + x(5).*k.*w;

missing close bracket

has same issue as before with minima at 0

[Anand Ra]

@Walter Roberson@Matt J

I think I missed the relationship constaints. I have included that now. I am not sure how to construct the minimization part, given my relationshipo constrains

% Objective:Optimize the lengths to minimze the power using a new variable.

a = 0.1:20;
b = 0.1:20;
d = a + 0.1:20;
c = b + 0.1:20;
e = d + 0.1:20

%Constants
k= 2;
w=1;
v=1.5
%Variables

AB = sqrt(a.^2 + b.^2);
BC = sqrt( c.^2 + ((e-d)/2).^2 );
CS = sqrt( c.^2 + ((e-d)/2).^2 );


VAB = sqrt(((((a.*v).^2/(((b.^2).*4))) + (v^2)/2 )));
% VBS = sqrt(((a*v)^2/((4*b*b)) + (v^2)/2 ));
VCS = ((2*c)./(e-d)).*sqrt(AB.^2);
VBC= CS.^2 + BC.^2;



%Actual Power
 %P = (AB*VAB + BC*VBC + CS*VCS)*k*w; % Power
%
% Objective
%To search and find the values for a, b, c d and eto minimize power


% Not sure how to write the function for above

% fun = @(x)(x(:,1) + x(:,2) + x(:,3) + x(:,4) + x(:,5)).*k.*w;
% 
% [X1, X2, X3, X4, X5] = ndgrid(0:.1:2); % Should I give this condition in a nested loop?
% 
% X = [X1(:), X2(:), X3(:), X4(:), X5(:)];
% 
% P = fun(X);
% [bestP, idx] = min(P(:))
% best_X = X(idx,:)