Minimizing a function in one variable in Matlab

In summary, the conversation discusses a multi-objective problem and how it can be transformed using scalarization. The objective is to minimize the expression -p'*x + u*x'*V*x, subject to the constraint 1*x=1. The variables involved are -u (risk aversion index), V (4x4 variance covariance matrix), p (4x1 expected return vector), and x (4x1 asset weight vector). The goal is to vary -u from 0.1 to 100. The speaker has tried using the fmincon function but is unsure of how to set it up. They are looking for additional help and information.
  • #1
vasqueza34
1
0
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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  • #2
I'm sorry you are not finding help at the moment. Is there any additional information you can share with us?
 

1. What is the purpose of minimizing a function in one variable in Matlab?

The purpose of minimizing a function in one variable in Matlab is to find the input value that results in the lowest output value of the function. This is useful in many areas of science and engineering, such as optimization problems and data analysis.

2. How do I define a function in Matlab?

To define a function in Matlab, use the "function" keyword followed by the name of the function and the input variable. Then, use the "end" keyword to indicate the end of the function. For example:
function y = myFunction(x)
y = x^2;
end

3. How do I minimize a function in one variable using Matlab?

To minimize a function in one variable using Matlab, you can use the "fminbnd" function. This function takes in the function you want to minimize, as well as the lower and upper bounds of the input variable. It then returns the value of the input variable that results in the minimum output value of the function.

4. Can I plot the function and its minimum value in Matlab?

Yes, you can plot the function and its minimum value in Matlab by using the "plot" function. You can also use the "hold on" and "plot" functions to add the minimum value as a point on the plot. This can help visually verify the minimum value of the function.

5. Are there any other methods for minimizing a function in one variable in Matlab?

Yes, there are other methods for minimizing a function in one variable in Matlab such as the "fminsearch" function or using optimization algorithms like gradient descent. However, the "fminbnd" function is often the most efficient and accurate method for minimizing a function in one variable in Matlab.

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