Optimisation of function containing matrix

2019 10 10
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更新时间：2019 10 11
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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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Fabio Freschi
Fabio Freschi 2019-10-10
编辑：Fabio Freschi 2019-10-10
Can you share C and v?
Isabelle Steinmann
Isabelle Steinmann 2019-10-10
C =
Columns 1 through 10
1.0003 0.0245 0.0052 0.0172 0.0273 0.0220 0.0171 0.0208 0.0073 0.0218
0.0054 0.9994 0.0100 0.0326 0.0329 0.0369 0.0173 0.0155 0.0224 0.0269
0.0152 0.0097 1.0001 0.0173 0.0374 0.0220 0.0222 0.0208 0.0174 0.0219
0.0001 -0.0000 0.0000 1.0005 0.0255 0.0054 0.0103 0.0101 0.0007 0.0057
0.0001 -0.0000 0.0000 0.0056 1.0006 0.0103 0.0052 0.0050 0.0055 0.0204
0.0001 -0.0003 -0.0000 0.0059 0.0108 1.0007 0.0009 -0.0097 0.0156 0.0054
0.0001 -0.0001 -0.0000 0.0112 0.0110 0.0255 1.0005 0.0001 0.0359 0.0105
0.0001 -0.0001 -0.0000 0.0112 0.0110 -0.0041 0.0257 1.0004 0.0262 0.0156
0.0000 -0.0003 -0.0000 0.0205 0.0008 0.0005 0.0005 0.0002 1.0005 0.0003
0.0001 -0.0001 -0.0000 0.0157 0.0011 0.0105 0.0056 0.0053 0.0108 1.0004
0.0001 -0.0002 -0.0000 0.0111 0.0210 0.0157 0.0162 0.0152 0.0213 0.0009
0.0000 -0.0003 -0.0000 0.0107 0.0154 0.0007 0.0150 -0.0000 0.0155 0.0054
0.0050 -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
0.0000 -0.0101 -0.0001 0.0102 0.0054 0.0151 0.0006 -0.0099 0.0002 0.0001
0.0100 -0.0000 0.0000 0.0158 0.0309 0.0058 0.0007 0.0005 0.0057 0.0158
Columns 11 through 16
0.0213 0.0179 0.0317 0.0165 0.0165 0.0064
0.0068 0.0479 0.0367 0.0270 0.0316 0.0213
0.0216 0.0228 0.0316 0.0167 0.0164 0.0163
0.0005 0.0055 0.0002 0.0003 0.0002 0.0155
0.0007 0.0007 0.0003 0.0003 0.0002 0.0203
0.0152 0.0307 0.0204 0.0109 0.0107 0.0002
0.0158 0.0264 0.0008 0.0110 0.0007 0.0104
0.0158 0.0212 0.0054 0.0009 0.0055 0.0106
0.0149 0.0205 0.0053 0.0203 0.0053 0.0002
0.0205 0.0060 0.0056 0.0005 0.0054 0.0152
1.0009 0.0214 0.0204 0.0010 0.0058 0.0006
0.0002 1.0008 0.0004 0.0153 0.0200 0.0005
0.0159 0.0169 1.0008 0.0257 0.0202 0.0009
-0.0150 0.0041 0.0043 0.9998 -0.0103 -0.0002
0.0002 0.0151 0.0199 0.0004 1.0003 -0.0000
0.0154 0.0108 0.0057 0.0104 0.0054 1.0008
v is a zero vector
Fabio Freschi
Fabio Freschi 2019-10-11
It is better to attach data as mat file

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 采纳的回答

Fabio Freschi
Fabio Freschi 2019-10-10
编辑：Fabio Freschi 2019-10-11

0 个投票

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
>> mo
mo =
0.0549
0.0481
0.0524
0.0668
0.0672
0.0644
0.0615
0.0627
0.0661
0.0655
0.0623
0.0653
0.0570
0.0737
0.0689
0.0633
>> sum(mo)
ans =
1
>> C*mo
ans =
0.0720
0.0720
0.0720
0.0720
0.0720
0.0720
0.0720
0.0720
0.0720
0.0720
0.0720
0.0720
0.0720
0.0720
0.0720
0.0720

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Isabelle Steinmann
Isabelle Steinmann 2019-10-10
Will this work though? The variable I am optimising is mo and x is a function of mo.
So the optimisation constraint is Aeq.mo=beq
So that would give mo(1)=...=mo(16) but i was x(1)=...=x(16) where x=C*mo+v
Sorry, I know my choice of variables makes this confusing
Fabio Freschi
Fabio Freschi 2019-10-11
You are right, sorry for the misunderstanding. I edited the answer
Fabio Freschi
Fabio Freschi 2019-10-11
Isabelle, is it what you want?
Isabelle Steinmann
Isabelle Steinmann 2019-10-11
Yes, that's perfect. Thank you

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