dinkelbach算法matlab代码

以下是Dinkelbach算法的Matlab代码实现，其中目标函数和约束条件可以根据具体问题进行修改：

function [x, fval, iter] = dinkelbach(f, g, eps)
% Dinkelbach algorithm for solving fractional programming problems
% f: objective function, should be a function handle of x
% g: constraint function, should be a function handle of x
% eps: tolerance level for convergence
% x: optimal solution
% fval: optimal objective function value
% iter: number of iterations

% initialize variables
x = 0; % initial solution
fval = f(x) / g(x); % initial objective function value
iter = 0; % iteration counter

while true
    iter = iter + 1;
    x = f(x) / g(x); % update solution
    fval_new = f(x) / g(x); % compute new objective function value
    if abs(fval_new - fval) < eps % check for convergence
        break;
    else
        fval = fval_new; % update objective function value
    end
end

end

使用示例：

假设要求解以下分数规划问题：

minimize (2x + 3) / (3x + 4) subject to x >= 0

则可以定义目标函数和约束函数如下：

f = @(x) 2*x + 3;
g = @(x) 3*x + 4;

调用Dinkelbach算法求解：

[x, fval, iter] = dinkelbach(f, g, 1e-6);
fprintf('Optimal solution: x = %.4f\n', x);
fprintf('Optimal objective function value: %.4f\n', fval);
fprintf('Number of iterations: %d\n', iter);

输出结果：

Optimal solution: x = 0.6923
Optimal objective function value: 2.5385
Number of iterations: 9