Scaling in optimization problems
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Sargondjani
el 22 de En. de 2023
Assume a simple example, with an optimization problem:max
subject to
, with
and
given. I want to solve it with fmincon (because there will be other constraints as well), but with
the derivate with dV/dc will get ever smaller with t.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1270970/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1270975/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1270980/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1270985/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1270990/image.png)
A similar problem occurs when we have:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1270995/image.png)
Is there a way to scale the problem such that the derivates will be of similar size? Otherwise the solution for large t (or smalle alpha) will be less accurate, right?
(One work around would be to use a value function, and solve for each t, but I don't want to do that).
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Matt J
el 22 de En. de 2023
Editada: Matt J
el 22 de En. de 2023
the derivate with dV/dc will get ever smaller with t.
It's not clear that that matters because the values of c are also influenced by the constraints and their derivatives.
Regardless, though, most fmincon algorithms are Newton-like, which means they already normalize dV/dc by second derivatives.
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