Optimization variable which takes input in the form of matrix or vectors

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Mondeep maz 2018-8-8

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回答： J. Alex Lee 2018-8-8

I need to multiply a 100×48 matrix with a 48×1 vector and the sum of the elements of the resultant vector is the objective function. Is it possible that i can model the optimization variables as the columns of the 100×48 matrix?. If so how to write the bounds and objective function. I am using ga solver.

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Walter Roberson 2018-8-8

To confirm, you are optimizing on 4800 variables?

Mondeep maz 2018-8-8

4800 variables arranged in a matrix of 100×48

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Answer 1

J. Alex Lee 2018-8-8

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That doesn't seem like a mathematically well-posed optimization problem...but in general Matlab's fminX routines are multidimensional. Maybe you can just reshape to achieve your goal?

 x0 = rand(100,48) % initial guess of unknowns to solve for
 y = rand(48,1) % your parameters governing the optimization
 x = fminX(@(x)objFn(x,y),x0(:)) %
 function r = objFn(x,y)
   x = reshape(x,100,48); % or compute the correct dimensions based on numel(x) and length(y)
   r = sum(x*y); % or do you want sum(abs(x*y))?
 end

you would similarly reshape your bounds into vectors.

Or, a quick search reveals that Matlab's fminX functions actually do accept matrix arguments: https://www.mathworks.com/help/optim/ug/matrix-arguments.html.