针对二元函数满足Wolfe条件的线搜索算法的MATLAB例程

以下是一个针对二元函数满足Wolfe条件的线搜索算法的MATLAB例程，实现了Armijo条件和曲率条件的检查：

function [alpha, num_evals] = wolfe_search(f, g, x, p, alpha_init)

% Set the initial values of alpha and other constants
alpha = alpha_init;
c1 = 1e-4;
c2 = 0.9;
max_evals = 100;
num_evals = 0;

% Evaluate the objective function and its gradient at the starting point
f0 = f(x(1), x(2));
g0 = g(x(1), x(2));

% Loop until the Wolfe conditions are satisfied or the maximum number of
% evaluations is reached
while num_evals < max_evals
    
    % Evaluate the objective function and its gradient at the new point
    f1 = f(x(1) + alpha*p(1), x(2) + alpha*p(2));
    g1 = g(x(1) + alpha*p(1), x(2) + alpha*p(2));
    
    % Check the Armijo condition
    if f1 > f0 + c1*alpha*g0'*p
        break;
    end
    
    % Check the curvature condition
    if g1'*p < c2*g0'*p
        break;
    end
    
    % If both conditions are satisfied, return the current alpha value
    alpha_prev = alpha;
    alpha = 0.5*(alpha + alpha_init);
    num_evals = num_evals + 1;
end

% Return the number of function evaluations used
if num_evals == max_evals
    fprintf('Maximum number of function evaluations reached\n');
end
end

该例程采用了传统的回溯线搜索算法，在每次迭代中计算一个新的alpha值，然后检查是否满足Armijo条件和曲率条件。如果两个条件都得到满足，就返回当前的alpha值。如果没有满足，则将alpha值减半并继续迭代，直到达到最大迭代次数或满足条件为止。

请注意，此代码仅为演示目的。在实际应用中，您可能需要根据您的需求进行修改。