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- W4225526691 abstract "In this paper we consider large-scale composite optimization problems having the objective function formed as a sum of two terms (possibly nonconvex), one has block coordinate-wise Lipschitz continuous gradient and the other is differentiable but nonseparable. Under these general settings we derive and analyze two new random coordinate descent methods. The first algorithm, referred to as random coordinate proximal gradient method, considers the composite form of the objective function, while the other algorithm disregards the composite form of the objective and uses the partial gradient of the full objective, yielding a random coordinate gradient descent scheme with novel adaptive stepsize rules. We prove that these new stepsize rules make the random coordinate gradient scheme a descent method, provided that additional assumptions hold for the second term in the objective function. We also present a complete worst-case complexity analysis for these two new methods in both, convex and nonconvex settings. Preliminary numerical results also confirm the efficiency of our two algorithms on practical problems." @default.
- W4225526691 created "2022-05-05" @default.
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- W4225526691 date "2022-03-27" @default.
- W4225526691 modified "2023-09-23" @default.
- W4225526691 title "Random coordinate descent methods for nonseparable composite optimization" @default.
- W4225526691 doi "https://doi.org/10.48550/arxiv.2203.14368" @default.
- W4225526691 hasPublicationYear "2022" @default.
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