Vectorized gradient based optimizers

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mahmoud tarek 2019-12-30

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/498513-vectorized-gradient-based-optimizers

评论： Matt J 2020-1-15

采纳的回答： Matt J

Is there any vectorized gradient based optimizer available ? Even outside matlab ?

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Matt J 2019-12-31

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编辑：Matt J 2019-12-31

As long as you are willing to supply the gradient, you can vectorize the minimization of N objectives,

by applying fminunc to the consolidated objective,

or analogously with fmincon if each problem has constraints.

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mahmoud tarek 2020-1-4

编辑：mahmoud tarek 2020-1-4

在 MATLAB Online 中打开

This is the objective and nonlincon code

function OBJ = Obj(X)
OBJ = X(:,11);
end

and my NonLinCon function is

function [C, CEQ] = NonLinCon(X, NCHV, PCHV, IN_SPEC)
DOF.M(1).L = X(:,1);
 DOF.M(2).L = X(:,2);
 DOF.M(3).L = X(:,3);
 DOF.M(4).L = X(:,4);
 DOF.M(5).L = X(:,5);
 DOF.M(1).RHO = X(:,6);
 DOF.M(2).RHO = X(:,7);
 DOF.M(3).RHO = X(:,8);
 DOF.M(4).RHO = X(:,9);
 DOF.M(5).RHO = X(:,10);
 DOF.IB = X(:,11)*1e-3;
[~, OUT_SPEC] = aaSynFoldedPmosOL(NCHV,PCHV,DOF);
C(:,1) = IN_SPEC.UGF ./ double(OUT_SPEC.UGF) - 1;
C(:,2) = IN_SPEC.PM ./ double(OUT_SPEC.PM) - 1;
C(:,3) = log10(IN_SPEC.AVDC) ./ log10(double(OUT_SPEC.AVDC)) - 1;
C(:,4) = IN_SPEC.FO ./ double(OUT_SPEC.FO) - 1;
C(:,5) = IN_SPEC.FP1 ./ double(OUT_SPEC.FP1) - 1;
C(:,6) = IN_SPEC.VO_SWING ./ double(OUT_SPEC.VO_SWING) - 1;
CEQ =[]     

where in_spec are given by user and aaSynFoldedPmosOL is a function that calculates the constraints i have not yet given a grradient function for either nonlincon or obj functions i was using finite difference step size options to control the gradient.

my function is highly nonlinear so what kind of gradient should i provide ?

Thank you.

mahmoud tarek 2020-1-15

yes, i can and i am trying now to provide the gradients (if possible) of my simulations function.

Do you have any documents or ideas on how to do that ?

Matt J 2020-1-15

在 MATLAB Online 中打开

The chain rule,

https://en.wikipedia.org/wiki/Chain_rule#General_rule

If an analytical calculation is too difficult, you can also try your own vectorized finite difference method to find the Jacobian of your simulation function. From that, it should be easier to find the total derivative of your objective using the chain rule.

delta = small_number;
Y0=simulation(X); %
Jacobian=nan(size(X)); %to hold the result
for i=1:11
    
    Xp=X;
    Xp(:,i)=Xp(:,i)+delta;
    
    Yp=simulation(Xp);
    
    Jacobian(:,i)=(Yp(:,i)-Y0(:,i))/delta;
    
end