= Solution
A standard form of the <Zoutendijk theorem> assumes that $f$ is continuously differentiable and bounded below on the starting level set, that its <gradient> is Lipschitz on a neighborhood of that set, and that the steps satisfy fixed <Wolfe conditions>. For <descent directions> $p_k$, define
$$
\cos\theta_k=-\frac{\nabla f(x_k)^Tp_k}{\|\nabla f(x_k)\|\,\|p_k\|}.
$$
Then
$$
\boxed{\sum_k\cos^2\theta_k\,\|\nabla f(x_k)\|^2<\infty.}
$$
In particular, if $\cos\theta_k\geq\delta>0$, then $\nabla f(x_k)\to0$. This last angle hypothesis is needed to turn the general descent theorem into <gradient> <convergence>.
For this quadratic, $f\geq0$, the <Hessian matrix> is the constant <positive-definite matrix> $H$, and the <gradient> is globally Lipschitz with constant $L=2\max(c^{-2},d^{-2})$. Its level sets are compact. Thus all objective-function hypotheses hold; Wolfe holds for the exact steps with the parameters above. The direction hypothesis will be verified for alternating exact coordinate minimization in the next part.
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