MATLAB Minimizing a function in one variable in Matlab

AI Thread Summary
The discussion centers on transforming a multi-objective optimization problem into a scalarized form for asset allocation. The objective is to minimize a function that combines expected returns and risk, represented by a variance-covariance matrix. The problem involves varying a risk aversion index, u, between 0.1 and 100, while ensuring that the sum of asset weights, represented by vector x, equals 1. The user is seeking guidance on how to effectively implement this optimization using the fmincon function, indicating a need for clarification on setup and constraints in the context of MATLAB or similar computational tools.
vasqueza34
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This problem was 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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