Matlab中能否从fminsearch获取Jacobian？求可行解决方法

Hey there! I get why you'd want a Jacobian output similar to lsqnonlin—it's super handy for post-optimization analysis. Let's break down the core issue first, then walk through practical solutions:

Why fminsearch doesn't return a Jacobian #

fminsearch relies on the Nelder-Mead simplex method, which is a derivative-free optimization algorithm. It never computes or stores Jacobian/gradient information during its process—so setting 'Jacobian','on' in optimset has no effect here. That option is only designed for derivative-based solvers like fminunc or lsqnonlin, which actively use Jacobian data to guide optimization.

Solutions to get Jacobian information #

1. Compute a numerical Jacobian manually after optimization

Since fminsearch gives you the optimized parameters, you can calculate a numerical Jacobian using finite differences. Here's a quick implementation tailored for residual-based functions (like you'd use with lsqnonlin):

function jacobian = compute_numerical_jacobian(residual_fun, x_opt, epsilon)
    num_params = length(x_opt);
    residual_base = residual_fun(x_opt);
    num_residuals = length(residual_base);
    
    jacobian = zeros(num_residuals, num_params);
    
    for i = 1:num_params
        % Perturb the i-th parameter slightly
        x_perturbed = x_opt;
        x_perturbed(i) = x_perturbed(i) + epsilon;
        
        % Calculate perturbed residual
        residual_perturbed = residual_fun(x_perturbed);
        
        % Finite difference approximation for the column
        jacobian(:, i) = (residual_perturbed - residual_base) / epsilon;
    end
end

% Usage example after running fminsearch:
[x_opt, fval, exitflag, output] = fminsearch(@your_residual_fun, x0, options);
jacobian = compute_numerical_jacobian(@your_residual_fun, x_opt, 1e-6);

Tweak epsilon based on your problem's scale—smaller values aren't always better, as they can introduce numerical noise.

2. Switch to a derivative-based solver (if feasible)

If your problem allows it, use lsqnonlin (for least-squares problems) or fminunc (for general unconstrained optimization) instead. These solvers natively support computing and returning Jacobians when you enable the 'Jacobian' option. For example:

options = optimset('MaxFunEvals',100,'Jacobian','on');
[x, residualsNorm, residual, exitflag, output, lambda, jacobian] = lsqnonlin(@your_residual_fun, x0, lb, ub, options);

This is the most straightforward approach if derivative-based optimization works for your problem.

内容的提问来源于stack exchange，提问作者Adnan j