Optimization of the weighted average sum of matrix norms in the workspace using the Optimization Tool
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There are workspace from three 3x3 matrices with random elements:
A=rand(3,3);
B=rand(3,3);
C=rand(3,3);
There are 9 vectors of the following form:
u1=[cos(a);sin(a);1-cos(0)]
u2=[cos(a);sin(a);1-cos(2*pi/3)]
u3=[cos(a);sin(a);1-cos(-2*pi/3)]
v1=[sin(b)*cos(C);sin(a);-cos(0)-1]
v2=[sin(b)*cos(C);sin(a);-cos(2*pi/3)-1]
v3=[sin(b)*cos(C);sin(a);-cos(-2*pi/3)-1]
w1=[cos(A);sin(B);-sin(0)]
w2=[cos(A);sin(B);-sin(2*pi/3)]
w3=[cos(A);sin(B);-sin(-2*pi/3)]
here
- variables;
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1077620/image.png)
The matrix of the following form is formed from the vectors:
J=[cross(v1,w1)/dot(cross(u1,v1),w1) cross(v2,w2)/dot(cross(u2,v2),w2) cross(v3,w3)/dot(cross(u3,v3),w3)];
Problem: We need to find parameters
that minimize the weighted average sum of matrix J norms at each of the workspace points, i.e.:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1077625/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1077630/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1077635/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1077640/image.png)
How to solve this problem using Optimization Tool ?
2 Comments
Matt J
on 26 Jul 2022
Edited: Matt J
on 26 Jul 2022
There are 9 vectors of the following form:
If A,B,C are 3x3 matrices and a,b are scalars, then v and w cannot be vectors. Nor can you run the code you've posted without concatenation error messages.
A=rand(3,3);
B=rand(3,3);
C=rand(3,3);
a=pi; b=pi;
u1=[cos(a);sin(a);1-cos(0)]
u2=[cos(a);sin(a);1-cos(2*pi/3)]
u3=[cos(a);sin(a);1-cos(-2*pi/3)]
v1=[sin(b)*cos(C);sin(a);-cos(0)-1]
v2=[sin(b)*cos(C);sin(a);-cos(2*pi/3)-1]
v3=[sin(b)*cos(C);sin(a);-cos(-2*pi/3)-1]
w1=[cos(A);sin(B);-sin(0)]
w2=[cos(A);sin(B);-sin(2*pi/3)]
w3=[cos(A);sin(B);-sin(-2*pi/3)]
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