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• W3204197457 abstract "Block coordinate descent (BCD), also known as nonlinear Gauss-Seidel, is a simple iterative algorithm for nonconvex optimization that sequentially minimizes the objective function in each block coordinate while the other coordinates are held fixed. We propose a version of BCD that, for block multi-convex and smooth objective functions under constraints, is guaranteed to converge to the stationary points with worst-case rate of convergence of $O((log n)^{2}/n)$ for $n$ iterations, and a bound of $O(epsilon^{-1}(log epsilon^{-1})^{2})$ for the number of iterations to achieve an $epsilon$-approximate stationary point. Furthermore, we show that these results continue to hold even when the convex sub-problems are inexactly solved if the optimality gaps are uniformly summable against initialization. A key idea is to restrict the parameter search within a diminishing radius to promote stability of iterates. As an application, we provide an alternating least squares algorithm with diminishing radius for nonnegative CP tensor decomposition that converges to the stationary points of the reconstruction error with the same robust worst-case convergence rate and complexity bounds. We also experimentally validate our results with both synthetic and real-world data and demonstrate that using auxiliary search radius restriction can in fact improve the rate of convergence." @default.
• W3204197457 created "2021-10-11" @default.
• W3204197457 creator A5065059104 @default.
• W3204197457 date "2020-12-07" @default.
• W3204197457 modified "2023-09-27" @default.
• W3204197457 title "Convergence and complexity of block coordinate descent with diminishing radius for nonconvex optimization." @default.
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• W3204197457 hasPublicationYear "2020" @default.
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