Quasi Newton optimization for a function

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Manfrid Loper 2020-3-2

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/508634-quasi-newton-optimization-for-a-function

评论： J. Alex Lee 2020-3-3

Im trying to implement Quasi Newton method to optimize a function. the code so far has two problematic issues that I pointed out in the script (where alpha need to be calculated and also B and Binve be updated), Can someone please help me implement formulas mentioned in Optimization_problem, so i can run the script successfully. Here what i have so far. Thanks very much!

clc;clear;
% objective function, its gradient and Hessian
f = @(x1,x2) -4*x1 - 2*x2 - x1.^2 + 2*x1.^4 - 2*x1.*x2 + 3*x2.^2;
Gradient = @(x) [-4-2*x(1)+8*x(1)^3-2*x(2);  -2-2*x(1)+6*x(2);];
%Hessian  = @(x) [-2+24*x(1)^2, -2; -2; 6];
% plot contour lines
[X, Y] = meshgrid(-0.25:0.01:1.75, -0.25:0.0025:1.75); 
contour(X,Y,f(X,Y),[-4.34 -4.3 -4.2 -4.1 -4.0 -3 -2 -1 0],'ShowText','On'), hold on; 
grid on;
% initialization
x0 = [0; 0;];  
df0 = Gradient(x0);
B = eye(2);
invB = eye(2);
% store intermediate points
Xs(:,1) = x0;
for i = 1:500
    % compute step size "alpha"
    %
    % %% problematic part 
    % update x
    x1 = x0 - alpha*invB*df0;
    df1 = Gradient(x1);
    fprintf('It. %i: f(%e,%e) = %e.\n', i, x1(1), x1(2), f(x1(1),x1(2)));
    Xs(:,i+1) = x1;
    % check the stopping criterion.
    if norm(x1-x0)/norm(x1)<1e-4
        break;
    end
    % update B and invB
    %
    %problematic part 
    %
    % update x0 and df0
    x0  = x1;
    df0 = df1;
end
plot(Xs(1,:), Xs(2,:),'o-');
daspect([1 1 1]);
hold off;