How to make a matrix compose by seperate optimization variables

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BOWEN LI
BOWEN LI 2019-7-2
编辑： Matt J 2019-7-3
Hi everyone,
I am thinking if it possible to put several optimizaiton variables into a matrix form. My optimization variable is defined by this syntax:
>> z1=optimvar('z1','Type','integer','LowerBound',0,'UpperBound',1)
>> z2=optimvar('z2','Type','integer','LowerBound',0,'UpperBound',1)
>> z3=optimvar('z3','Type','integer','LowerBound',0,'UpperBound',1)
zij=['z1','z2','z3';'z2','z2','z3';'z3','z3','z3']
It turns out that my 'zij' is a set of arrays not matrix. Anyone has idea about that? Thanks so much!

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Matt J
Matt J 2019-7-2
This works fine, once you remove the quotes
>> zij=[z1,z2,z3; z2,z2,z3; z3,z3,z3];
>> showexpr(zij)
(1, 1)
z1
(2, 1)
z2
(3, 1)
z3
(1, 2)
z2
(2, 2)
z2
(3, 2)
z3
(1, 3)
z3
(2, 3)
z3
(3, 3)
z3
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Matt J
Matt J 2019-7-3
编辑：Matt J 2019-7-3
If all the matrix elements Zmatrix(i,j) were independent variables, you could do so as follows,
Zmatrix=optimvar('optimv',[3,3],'Type','integer','LowerBound',0,'UpperBound',1);
However, in your posted example, the Zmatrix(i,j) were not all independent of each other.
You can create a "dependent optimization variable" for your posted example like this,
z=optimvar('z',[3,1],'Type','integer','LowerBound',0,'UpperBound',1);
Zmatrix=z([ 1 2 3; 2,2,3;3 3 3]);
So, note that this Zmatrix object is of type OptimizationVariable,
Zmatrix =
3×3 OptimizationVariable array with properties:
Read-only array-wide properties:
Name: 'z'
Type: 'integer'
IndexNames: {{} {}}
Elementwise properties:
LowerBound: [3×3 double]
UpperBound: [3×3 double]
Reference to a subset of OptimizationVariable with Name 'z'.
however, it is really just a matrix of pointers, basically, to different z(i). It has no independence existence of its own. In particular, if you modify Z(1,2).LowerBound, then Z(2,1).LowerBound and Z(2,2).LowerBound will change as well, because we defined all three to be aliases of the same independent variable z(2). For additional reading,
https://www.mathworks.com/help/optim/ug/optim.problemdef.optimizationexpression.html#mw_c5c5017a-4e36-4d39-bba2-649713ac7415
BOWEN LI
BOWEN LI 2019-7-3
Hi, I think the dependent optimization variable you said "Zmatrix" is just what I want.
Because my goal is to let Z(1,2) and Z(2,1) have the same upperbound and lowerbound while Z(1,2) and Z(2,1) reference to the same independent variable z(2). So in this case, I can multiply 'Zmatrix' with the other matrix which I also index as [1 2 3; 2,2,3;3 3 3].
So, in this sense, Z(1,3),Z(3,1),Z(3,2), and Z(3,3) all reference to z(3) right?
Thank you so much!

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