= Convergence of primal-dual hybrid gradient
{title2=$\tau\sigma\|D\|^2<1$}
For proper <lower semicontinuous> <convex functions> on finite-dimensional <Hilbert spaces>, a nonempty <saddle point> set, and constant positive steps satisfying the displayed inequality, the <primal-dual hybrid gradient method> with extrapolation parameter one converges to a saddle point. The strict condition controls the bilinear coupling by the <operator norm>. It does not remove the need for existence of a saddle point. The fixed-step theorem and assumptions are recalled in https://arxiv.org/pdf/1608.08883[Malitsky and Pock, A first-order primal-dual algorithm with linesearch, Section 1].
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