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• W3208317188 abstract "This paper studies quasi-Newton methods for solving strongly-convex-strongly-concave saddle point problems (SPP). We propose greedy and random Broyden family updates for SPP, which have explicit local superlinear convergence rate of ${mathcal O}big(big(1-frac{1}{nkappa^2}big)^{k(k-1)/2}big)$, where $n$ is dimensions of the problem, $kappa$ is the condition number and $k$ is the number of iterations. The design and analysis of proposed algorithm are based on estimating the square of indefinite Hessian matrix, which is different from classical quasi-Newton methods in convex optimization. We also present two specific Broyden family algorithms with BFGS-type and SR1-type updates, which enjoy the faster local convergence rate of $mathcal Obig(big(1-frac{1}{n}big)^{k(k-1)/2}big)$. Additionally, we extend our algorithms to solve general nonlinear equations and prove it enjoys the similar convergence rate." @default.
• W3208317188 created "2021-11-08" @default.
• W3208317188 creator A5073257809 @default.
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• W3208317188 date "2021-11-04" @default.
• W3208317188 modified "2023-10-16" @default.
• W3208317188 title "Quasi-Newton Methods for Saddle Point Problems and Beyond" @default.
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• W3208317188 doi "https://doi.org/10.48550/arxiv.2111.02708" @default.
• W3208317188 hasPublicationYear "2021" @default.
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