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How to minimize a vectorized function in 1 variable?
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This problem is originally a multi objective problem but using scalarization it can be transformed to the following:
Min: -p'*x + u*x'*V*x
subject to 1*x=1
u is the risk aversion index that I wish to vary from .1 to 100
V is a (4x4) variance covariance matrix
p is the (4x1) expected return vector, p' is (1x4)
x is the (4x1) asset weight vector I wish to solve for
** the sum of x is 1 (the only constraint)
I've tried the fmincon function but don't know how to set it up.
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