How can I use outputs of the objective function as the equality constraints in fmincon

Question

Robert Dibble 2016-1-19

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https://ww2.mathworks.cn/matlabcentral/answers/264363-how-can-i-use-outputs-of-the-objective-function-as-the-equality-constraints-in-fmincon

回答： Alan Weiss 2016-1-19

BEMT_forward.m

I have a function: function [power,imbalance]=obj(trim) which I shan't include as it's very long.

trim=[rotorspeed bladepitch diskangle] and these parameters (along with some constants) are used to calculate the amount of power required (power); the difference between vertical thrust and weight (imbalance(1)) and the difference between horizontal thrust and drag (imbalance(2)).

What I want to do is minimise the power subject to imbalance=[0 0] but I'm struggling to implement it with fmincon. What I currently have is a very bad bodge. I have 2 copies of the function: 1 only outputs power and is the objective function and the other is used for the @nonlcon option where imbalance is used as equality constraint (ceq).

Ideally I'd like to have just one master function for both but as fmincon uses the first output of the objective function to minimise and it uses the first 2 outputs of the @nonlcon function for the contraints I can't; unless I have a way of differentiating between whether the function is being used as an objective function or as a @nonlcon function.

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jgg 2016-1-19

在 MATLAB Online 中打开

I don't know if I can completely solve your problem, but you could do the following:

 function [power] = objective(trim)
    [power,~] = obj(trim);
 end
 function [imbalance] = constraint(trim)
   [~,imbalance] = obj(trim);
end

(You can also wrap this in a function that selects the output, but I think that's un-necessary and hurts readability)

From here, you can call as usual. While this will certainly reduce the amount of code hanging around, it won't really save you all that much computational overhead.

A suggestion I thought might work is to set

global power imbalance

in your obj function then do the following:

 function [imbalance] = constraint(trim)
   global imbalance
 end

I'm not sure if this will work, since it depends when the constraint is called in the solver; but basically, you can exploit the fact that you can store variables globally to get the value of imbalance out of the objective function without evaluating it again.

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