Matlab中dinkelbachd算法代码

以下是Matlab中Dinkelbach算法的一个简单实现：

function [x, obj] = dinkelbach(f, g, epsilon)
% Dinkelbach algorithm for solving f(x) = t*g(x).
% Inputs:
% f: Function handle for the objective function f(x).
% g: Function handle for the constraint function g(x).
% epsilon: Tolerance for the relative error in the solution.
% Outputs:
% x: Solution vector.
% obj: Objective function value at the solution.

% Initialization
t = 1;
x = fmincon(@(x) -f(x), zeros(size(g, 2), 1), [], [], g, t, [], [], [], optimset('Display', 'off'));
obj = f(x) - t*g(x);

% Dinkelbach algorithm
while abs(obj) > epsilon*abs(f(x))
    t = f(x)/g(x);
    x = fmincon(@(x) -f(x), zeros(size(g, 2), 1), [], [], g, t, [], [], [], optimset('Display', 'off'));
    obj = f(x) - t*g(x);
end
end

其中，f和g分别是目标函数和约束函数的函数句柄，epsilon是相对误差容限。该算法的基本思想是不断调整t值，使得约束条件g(x)趋近于目标函数f(x)的值，从而求解目标函数的最优解x。