Optimisation of function containing matrix

Question

Isabelle Steinmann 2019-10-10

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/484564-optimisation-of-function-containing-matrix

评论： Isabelle Steinmann 2019-10-11

采纳的回答： Fabio Freschi

I am having trouble optimising this system. I have been trying to use fmincon without success.

C is a 16x16 matrix, mo and v and 1 are 16x1 vectors. I want to choose mo to maximise x = c*mo+v

The constraints are: the components of mo must add to one (I think I've done this one)

and each component of x should be equal, that is x1=x2=...=x16 where x=c*mo+v (I have no idea how to represent this)

fun = @(mo) -C*mo-v;
A=[];
b=[];
Aeq= ones(1,16);
beq= 1; 
lb = zeros(16,1);
ub = ones(16,1);
m0 = 1/16*ones(16,1);
mo = fmincon(fun,m0,A,b,Aeq,beq,lb,ub)

Please let me know where I'm going wrong...

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Isabelle Steinmann 2019-10-10

C =
  Columns 1 through 10
0003    0.0245    0.0052    0.0172    0.0273    0.0220    0.0171    0.0208    0.0073    0.0218
0054    0.9994    0.0100    0.0326    0.0329    0.0369    0.0173    0.0155    0.0224    0.0269
0152    0.0097    1.0001    0.0173    0.0374    0.0220    0.0222    0.0208    0.0174    0.0219
0001   -0.0000    0.0000    1.0005    0.0255    0.0054    0.0103    0.0101    0.0007    0.0057
0001   -0.0000    0.0000    0.0056    1.0006    0.0103    0.0052    0.0050    0.0055    0.0204
0001   -0.0003   -0.0000    0.0059    0.0108    1.0007    0.0009   -0.0097    0.0156    0.0054
0001   -0.0001   -0.0000    0.0112    0.0110    0.0255    1.0005    0.0001    0.0359    0.0105
0001   -0.0001   -0.0000    0.0112    0.0110   -0.0041    0.0257    1.0004    0.0262    0.0156
0000   -0.0003   -0.0000    0.0205    0.0008    0.0005    0.0005    0.0002    1.0005    0.0003
0001   -0.0001   -0.0000    0.0157    0.0011    0.0105    0.0056    0.0053    0.0108    1.0004
0001   -0.0002   -0.0000    0.0111    0.0210    0.0157    0.0162    0.0152    0.0213    0.0009
0000   -0.0003   -0.0000    0.0107    0.0154    0.0007    0.0150   -0.0000    0.0155    0.0054
0050   -0.0104   -0.0001    0.0213    0.0212    0.0164    0.0456    0.0151    0.0169    0.0159
   -0.0001   -0.0200   -0.0001    0.0095   -0.0004    0.0092   -0.0102   -0.0052   -0.0006    0.0047
0000   -0.0101   -0.0001    0.0102    0.0054    0.0151    0.0006   -0.0099    0.0002    0.0001
0100   -0.0000    0.0000    0.0158    0.0309    0.0058    0.0007    0.0005    0.0057    0.0158
  Columns 11 through 16
0213    0.0179    0.0317    0.0165    0.0165    0.0064
0068    0.0479    0.0367    0.0270    0.0316    0.0213
0216    0.0228    0.0316    0.0167    0.0164    0.0163
0005    0.0055    0.0002    0.0003    0.0002    0.0155
0007    0.0007    0.0003    0.0003    0.0002    0.0203
0152    0.0307    0.0204    0.0109    0.0107    0.0002
0158    0.0264    0.0008    0.0110    0.0007    0.0104
0158    0.0212    0.0054    0.0009    0.0055    0.0106
0149    0.0205    0.0053    0.0203    0.0053    0.0002
0205    0.0060    0.0056    0.0005    0.0054    0.0152
0009    0.0214    0.0204    0.0010    0.0058    0.0006
0002    1.0008    0.0004    0.0153    0.0200    0.0005
0159    0.0169    1.0008    0.0257    0.0202    0.0009
   -0.0150    0.0041    0.0043    0.9998   -0.0103   -0.0002
0002    0.0151    0.0199    0.0004    1.0003   -0.0000
0154    0.0108    0.0057    0.0104    0.0054    1.0008
    
    v is a zero vector

Fabio Freschi 2019-10-11

It is better to attach data as mat file

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Answer 1

Fabio Freschi 2019-10-10

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/484564-optimisation-of-function-containing-matrix#answer_395703

编辑：Fabio Freschi 2019-10-11

While waiting for the data, I try to solve one of the questions. you can set the missing constraint as

x1-x2 = 0

x2-x3 = 0

...

so, let's call M the matrix with +1 -1 along the diagonal

M = diag(ones(16,1),0)+diag(-ones(15,1),1);

The last row has to be removed

% remove last row
M = M(1:end-1,:);

now, x = C*mo+v and we want M*x = 0, so Mx = M*C*mo+M*v = 0 and the new equality constraint is

% new constraints
Aeq2 = M*C;
beq2 = -M*v;
% append
Aeq = [Aeq; Aeq2];
beq = [beq; beq2];

However, the main problem is that your objective function returns a vector and not a scalar quantity. I don't know your problem but is the sum of all x a feasible objective function to maximize?

fun = @(mo) -sum(C*mo+v);

In this case the solution is