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Optimization of an objective function with matrix as a variable

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Akash
Akash 2014-5-15
评论： Matt J 2014-5-15
I have a function to be maximized with takes as input a 100 x 100 matrix. How do i dynamically optimize this using optimization toolbox, i.e. varying the entire (100 x 100) matrix simultaneously [not cell by cell or row by row]. In addition, i also need to put constraint on every element of matrix. In short it becomes a single objective function, 10000 variables, 10001 constraints problem. Code attached (main & function) in which I want to optimize the Terminal_Wealth with constraint on variable alpha matrix [0<a(i,j)<1] & Risk<10 (--> this would be a non-linear constraint, I suppose).

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回答（1 个）

Matt J
Matt J 2014-5-15
编辑：Matt J 2014-5-15
This is probably what you're looking for
http://www.mathworks.com/help/optim/ug/matrix-arguments.html
Essentially, there is nothing stopping you from writing an objective function that takes a 100x100 matrix as input. However, if you have linear in/equality constraint matrix data A,b,Aeq,beq then A,Aeq will have 10000 columns and will be expected to be written so that
A*X(:)<=b
Aeq*X(:)=beq
are the constraints on a given 100x100 matrix X.
  2 个评论
Matt J
Matt J 2014-5-15
Maybe an example would be best. Suppose, I have a 2x2 matrix X and I want to minimize the sum over all the elements, subect to the constraints 0<=X(i,j)<=1 and
sum(X(i,j)^2)=1
Then I could do so as follows
nonlcon=@(X) deal([],norm(X(:))^2-1);
X= fmincon(@(X) sum(X(:)),rand(2),[],[],[],[],...
zeros(2), ones(2), nonlcon );

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