Is there a better function to minimize than fminsearch ?
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Hello, I would like to know if it exits a better function to minimize a function than fminsearch ? I have this line :
[X, fval, exitflag, output] = fminsearch(@func, X0, options, params)
I precise I have the optimization toolbox. Thank you for your help !
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Walter Roberson
2017년 10월 18일
Do you need a global optimization or a local optimization? Is the function differentiable? Is its Jacobian known? Is its Hessian known? If you were to pass symbolic variables into the function would it be able to return a symbolic formula in response ?
답변 (2개)
Birdman
2017년 10월 18일
There is a user-written function which contains Hooke-Jeeves algorithm. Maybe this will help you. The inputs and the outputs are clearly defined.
function [X,BestF,Iters] = hookejeeves(N, X, StepSize, MinStepSize, Eps_Fx, MaxIter, myFx)
% Function HOOKEJEEVS performs multivariate optimization using the
% Hooke-Jeeves search method.
%
% Input
%
% N - number of variables
% X - array of initial guesses
% StepSize - array of search step sizes
% MinStepSize - array of minimum step sizes
% Eps_Fx - tolerance for difference in successive function values
% MaxIter - maximum number of iterations
% myFx - name of the optimized function
%
% Output
%
% X - array of optimized variables
% BestF - function value at optimum
% Iters - number of iterations
%
Xnew = X;
BestF = feval(myFx, Xnew, N);
LastBestF = 100 * BestF + 100;
bGoOn = true;
Iters = 0;
while bGoOn
Iters = Iters + 1;
if Iters > MaxIter
break;
end
X = Xnew;
for i=1:N
bMoved(i) = 0;
bGoOn2 = true;
while bGoOn2
xx = Xnew(i);
Xnew(i) = xx + StepSize(i);
F = feval(myFx, Xnew, N);
if F < BestF
BestF = F;
bMoved(i) = 1;
else
Xnew(i) = xx - StepSize(i);
F = feval(myFx, Xnew, N);
if F < BestF
BestF = F;
bMoved(i) = 1;
else
Xnew(i) = xx;
bGoOn2 = false;
end
end
end
end
bMadeAnyMove = sum(bMoved);
if bMadeAnyMove > 0
DeltaX = Xnew - X;
lambda = 0.5;
lambda = linsearch(X, N, lambda, DeltaX, myFx);
Xnew = X + lambda * DeltaX;
end
BestF = feval(myFx, Xnew, N);
% reduce the step size for the dimensions that had no moves
for i=1:N
if bMoved(i) == 0
StepSize(i) = StepSize(i) / 2;
end
end
if abs(BestF - LastBestF) < Eps_Fx
break
end
LastBest = BestF;
bStop = true;
for i=1:N
if StepSize(i) >= MinStepSize(i)
bStop = false;
end
end
bGoOn = ~bStop;
end
function y = myFxEx(N, X, DeltaX, lambda, myFx)
X = X + lambda * DeltaX;
y = feval(myFx, X, N);
% end
function lambda = linsearch(X, N, lambda, D, myFx)
MaxIt = 100;
Toler = 0.000001;
iter = 0;
bGoOn = true;
while bGoOn
iter = iter + 1;
if iter > MaxIt
lambda = 0;
break
end
h = 0.01 * (1 + abs(lambda));
f0 = myFxEx(N, X, D, lambda, myFx);
fp = myFxEx(N, X, D, lambda+h, myFx);
fm = myFxEx(N, X, D, lambda-h, myFx);
deriv1 = (fp - fm) / 2 / h;
deriv2 = (fp - 2 * f0 + fm) / h ^ 2;
diff = deriv1 / deriv2;
lambda = lambda - diff;
if abs(diff) < Toler
bGoOn = false;
end
end
% end
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Birdman
2017년 10월 20일
편집: Birdman
2017년 10월 20일
Firstly, enter the following informations for the *hookejeeves* function.
N=..; X=[a1 .. a11]; StepSize=[0.5 .. 0.5]; MinStepSize=[0.01 .. 0.01]; Eps_Fx=[];%let it be empty
Then, save the following function with the name hookejeeves
function [X,BestF,Iters] = hookejeeves(N, X, StepSize, MinStepSize, MaxIter, myFx) %Başlangıç atamalarının yapılması. BestF=x(k+1), LastBestF=x(k) gibi %düşünülebilir. Xnew = X; BestF = feval(myFx, Xnew, N); LastBestF = 100 * BestF + 100; %bGoOn değişkenine bağlı while döngüsü, maksimum iterasyon sayısına veya %verilen toleransa ulaşılınca biter. bGoOn = true; Iters = 0; %Civar aramasının gerçekleştiği while döngüsüdür. while bGoOn Iters = Iters + 1; if Iters > MaxIter break; end X = Xnew; %N=2 değişken için arama yapılmaktadır. for i=1:N bMoved(i) = 0; bGoOn2 = true; while bGoOn2 xx = Xnew(i); Xnew(i) = xx + StepSize(i); F = feval(myFx, Xnew, N); if F < BestF BestF = F; bMoved(i) = 1; else Xnew(i) = xx - StepSize(i); F = feval(myFx, Xnew, N); if F < BestF BestF = F; bMoved(i) = 1; else Xnew(i) = xx; bGoOn2 = false; end end end end for i=1:N bMadeAnyMove(i) = sum(bMoved(i));%Civar araması başarılıysa, bMadeAnyMove(i) değişkeni 0'dan farklı olur. if bMadeAnyMove(i) > 0 Xnew1(i) = 2*Xnew(i) - X(i);%if bloğunda yeni x(k+1) değeri yukarıda kullanılmak üzere elde edilir. end end BestF = feval(myFx, Xnew1, N); LastBestF = feval(myFx, Xnew, N); %Fonksiyonun değeri bir öncekinden daha küçükse, bir önceki değerlerin %yeni x değerini bulurken kullanılması. for i=1:N if BestF < LastBestF Xnew(i)=Xnew1(i); X(i)=Xnew(i); Xnew1(i) = 2*Xnew(i) - X(i); end end %Civar araması başarısızsa, adım sayısı yarıya düşürülür. for i=1:N if bMoved(i) == 0 StepSize(i) = StepSize(i) / 2; end end %Adım sayısı, verilen adım sayısından daha küçük olursa iterasyon sonlanır. bStop = true; for i=1:N if StepSize(i) >= MinStepSize(i) bStop = false; end end bGoOn = ~bStop; end
Don't worry about the comment lines, they are in turkish. Then enter the following code:
hookejeeves(N,X,StepSize,MinStepSize,Eps_Fx,@intrafunc)
This one should work. Let me know the outcome. If you give 11 variables, it might take a little longer to calculate but do not worry and wait for it to get it done.
Alan Weiss
2017년 10월 18일
You might be interested in the Optimization Decision Table, which exists to help you choose the most appropriate solver.
Alan Weiss
MATLAB mathematical toolbox documentation
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