Question

我正在尝试使用fsolve函数在MATLAB中找到非线性系统的解决方案。我知道解决方案所在的区域，因此我的初始点是该区域内的随机变化。代码如下：

%MATLAB parameters
digits = 32;
format shortEng
%Initialization of solving process
min_norm = realmax;
options = optimoptions('fsolve', 'Algorithm', 'trust-region-dogleg',... 
    'Display', 'off', 'FunValCheck', 'on', 'Jacobian', 'on',...
    'DerivativeCheck', 'on');
%Solving loop
while 1
    %Refreshes seed after 100000 iterations
    rng('shuffle');
    for n=1:100000
        %Initial points are randomly placed in solving region
        x_0 = zeros(1, 3);
        x_0(1) = 20*(10^-3)+ abs(3*(10^-3)*randn);
        x_0(2) = abs(10^(-90) + 10^-89*randn);
        x_0(3) = abs(10*randn);
        %Solving
        [x, fval] = fsolve(@fbnd, x_0, options);
        norm_fval = norm(fval);
        %If norm is minimum, result is displayed
        if all(x > 0.0) && (norm_fval < min_norm)
            iter_solu = x;
            display(norm_fval);
            display(iter_solu);
            min_norm = norm_fval;
        end
    end
end

要优化的功能及其jacobian遵循：

function [F, J] = fbnd(x)
    F(1) = x(1) - x(2)*(exp(7.56/(1.5*0.025))-1);
    F(2) = x(1) - x(2)*(exp((x(3)*0.02)/(1.5*0.025))-1)-0.02;
    F(3) = x(1) - x(2)*(exp((6.06+x(3)*0.018)/(1.5*0.025))-1)-0.018;
    J = [[1.0, -3.5790482371355382991651020082214*10^87, 0.0];...
         [1.0, 1.0-exp((8/15)*x(3)),-(8/15)*x(2)*exp((8/15)*x(3))];...
         [1.0, 1.0-exp(0.48*x(3)+161.6), -0.48*x(2)*exp(0.48*x(3)+161.6)]];
end

当我打开DerivativeCheck时，我收到以下错误：

Objective function derivatives:
Maximum relative difference between user-supplied 
and finite-difference derivatives = 1.
  User-supplied derivative element (1,1):     1
  Finite-difference derivative element (1,1): 0

由于某种原因，事情dF（1）/ dx（1）应该是零而不是1，当它显然是1.所以我继续将J（1,1）替换为0，并且现在我遇到了与J（3,1）相同的问题：

Objective function derivatives:
Maximum relative difference between user-supplied 
and finite-difference derivatives = 1.
  User-supplied derivative element (3,1):     1
  Finite-difference derivative element (3,1): 0

因此，我将J（3,1）替换为0，它只捕获较小的精度错误。有没有解释为什么它认为J（1,1）和J（3,1）应该为零？这对我来说真的很奇怪。

DerivativeCheck在fsolve函数中失败（雅可比）

0 个答案: