Minimizing a function in one variable in Matlab

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SUMMARY

The discussion focuses on minimizing a function in one variable using MATLAB, specifically through the fmincon function. The problem involves a scalarized multi-objective optimization defined by the equation Min: -p'*x + u*x'*V*x, with constraints that the sum of asset weights x equals 1. The parameters include a risk aversion index u ranging from 0.1 to 100, a variance-covariance matrix V (4x4), and an expected return vector p (4x1). The user seeks guidance on properly setting up the fmincon function for this optimization task.

PREREQUISITES
  • Understanding of MATLAB programming and syntax
  • Familiarity with optimization concepts, particularly in finance
  • Knowledge of variance-covariance matrices and their applications
  • Experience with the fmincon function in MATLAB for constrained optimization
NEXT STEPS
  • Review MATLAB documentation on the fmincon function and its options
  • Study examples of multi-objective optimization and scalarization techniques
  • Learn about setting up and interpreting variance-covariance matrices in MATLAB
  • Explore risk aversion modeling in financial optimization contexts
USEFUL FOR

Quantitative analysts, financial engineers, and MATLAB users involved in optimization problems, particularly in asset management and portfolio optimization.

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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