# non-linear optimization over a frequency bandwidth

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Joseph on 5 Mar 2015
Commented: Chris McComb on 6 Mar 2015
Hi there,
Is it possible to optimize a function over a frequency bandwidth? Given I have a non-linear function say Vout(f) and I want to optimize (e.g. maximize the average voltage output) over a frequency bandwidth as a function of design variables and constraints.
Is there a way to do this and extend a single objective to multi-objectives?
I'm only aware of using fmincon over a single frequency...
Thanks,

Matt J on 5 Mar 2015
Edited: Matt J on 5 Mar 2015
You could look at the multi-objective solver fgoalattain to see if that suits what you are trying to do. The average voltage can be computed inside the objective function by filtering Vout(f) with a bandpass filter, parametrized by f1 and f2, and computing the average of the filter output. You just want to make sure that the filter result is differentiable in f1 and f2. Therefore, a rect window bandpass filter would not be suitable. You would need to compromise and use some sort of tapered window.
Joseph on 6 Mar 2015
Thanks for the input Matt. I'll have a go at that. I'll leave the question open for a little longer to see what happens when I try implementation.

Chris McComb on 5 Mar 2015
I think you can do exactly what you said: maximize the average voltage output.
Use fmincon, but write an objective function that computes the voltage output for several frequencies and returns the average. If certain frequencies are more important than others, you can even do a weighted average.
Would that work in your case? Maybe I'm not understanding your question completely.
Joseph on 6 Mar 2015
Hi Chris, yes they are. But first step I'm was looking at maximizing Vout over a frequency bandwidth. Then move onto the f1 and f2.
Chris McComb on 6 Mar 2015
In that case, I'm afraid I don't see a more elegant solution to your problem. For your first step, I think the brute force approach may be the only way to go. That is, directly computing the average and maximizing that.
When you move on to a multiobjective problem, you'll no longer have a single optimal solution. Instead, you'll have a set of optimal solutions known as a Pareto frontier. In the Pareto frontier, the quality of a solution is denoted by a length n, where n is the number of objective functions.
I've done some work with multi-objective optimization, and once again I'd recommend a somewhat brutish approach (I'm starting to recognize a pattern in my preferences). There are a number of ways to go about this, but the simplest is to re-define your objective function as a weighted combination of -f1, f2 and Vout. Solving the optimization problem with different weights will allow you to resolve different points on the Pareto frontier.
I'm happy to provide more information about any of the above. Sorry I couldn't offer a more elegant solution!

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