生成一段惯性松弛算法代码

以下是常见的惯性松弛算法代码：

def inertial_relaxation_algorithm(x0, f, grad_f, beta=0.5, alpha=0.1, max_iter=1000, tol=1e-8):
    """
    Inertial relaxation algorithm for solving unconstrained optimization problems.

    Parameters:
        x0: numpy array
            Initial solution vector.
        f: function
            Objective function.
        grad_f: function
            Gradient of the objective function.
        beta: float
            The inertia parameter.
        alpha: float
            The relaxation parameter.
        max_iter: int
            Maximum number of iterations.
        tol: float
            Tolerance for convergence.

    Returns:
        x_k: numpy array
            The optimal solution.
    """
    x_k = x0
    v_k = np.zeros_like(x_k)
    f_k = f(x_k)
    for k in range(max_iter):
        grad_f_k = grad_f(x_k)
        v_k = beta * v_k - alpha * grad_f_k
        x_k1 = x_k + v_k
        f_k1 = f(x_k1)
        if abs(f_k1 - f_k) < tol:
            break
        f_k = f_k1
        x_k = x_k1
    return x_k

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