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- W4286892000 abstract "We consider the problem of finding a saddle point for the convex-concave objective $min_x max_y f(x) + langle Ax, yrangle - g^*(y)$, where $f$ is a convex function with locally Lipschitz gradient and $g$ is convex and possibly non-smooth. We propose an adaptive version of the Condat-V~u algorithm, which alternates between primal gradient steps and dual proximal steps. The method achieves stepsize adaptivity through a simple rule involving $|A|$ and the norm of recently computed gradients of $f$. Under standard assumptions, we prove an $mathcal{O}(k^{-1})$ ergodic convergence rate. Furthermore, when $f$ is also locally strongly convex and $A$ has full row rank we show that our method converges with a linear rate. Numerical experiments are provided for illustrating the practical performance of the algorithm." @default.
- W4286892000 created "2022-07-25" @default.
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- W4286892000 date "2021-10-28" @default.
- W4286892000 modified "2023-10-16" @default.
- W4286892000 title "A first-order primal-dual method with adaptivity to local smoothness" @default.
- W4286892000 doi "https://doi.org/10.48550/arxiv.2110.15148" @default.
- W4286892000 hasPublicationYear "2021" @default.
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