Scaling in optimization problems

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Sargondjani
Sargondjani on 22 Jan 2023
Edited: Matt J on 22 Jan 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.
A similar problem occurs when we have:
, where alpha is close to zero.
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).

Accepted Answer

Matt J
Matt J on 22 Jan 2023
Edited: Matt J on 22 Jan 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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