Optimization when solving equation system

Question

dj1du 2022-5-27

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编辑： Matt J 2022-5-28

Good evening,

I'm trying to solve the following issue:

Given a vector

(n=50 elements), which is expanded in known basis functions

and known coefficients

according to

. I'd like to express v in an alternative known basis

with unknown coefficients

like

. I obtain all coefficients

via

, in which the basis transformation matrix T follows from solution of the matrix equation

with

containing the

as column vectors. This procedure works perfectly fine so far, with one exception: I'd like to ensure that

, so the maximum value of the alternative expansion should never be smaller than the one of the original expansion.

Can this be done by optimization when solving

for T in any way in Matlab?

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Answer 1

Matt J 2022-5-27

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编辑：Matt J 2022-5-27

fmincon with a nonlinear constraint would probably work, although because your constraint is non-differentiable, strictly speaking the problem doesn't satisfy fmincon's assumptions. It might be worth doing a preliminary step, where you replace your max constraint with,

for some

. Then, use that solution as the initial guess when you solve the original problem (which corresponds to

).

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dj1du 2022-5-28

Thank you very much for your response! I just had a look at the function fmincon, but to be honest I'm not quite sure how to use it. Could you please give a more detailed explanation on its usage or even an example code, which applies to my specific problem?