= Gradient ascent
{title2=$x_{n+1}=x_n+\eta_n\nabla J(x_n)$}
<Gradient ascent> seeks a maximum by stepping along the <gradient> of a differentiable objective. It is <gradient descent> applied to $-J$. Taylor expansion gives $J(x+\eta\nabla J)=J(x)+\eta\|\nabla J\|^2+O(\eta^2)$, so sufficiently small positive steps improve the objective when the <gradient> is nonzero. Line search, projection onto admissible controls, and noise-aware <gradient> estimates are common practical modifications; a local stationary result need not be globally optimal.
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