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- W4288727913 abstract "This study develops a fixed-time convergent saddle point dynamical system for solving min-max problems under a relaxation of standard convexity-concavity assumption. In particular, it is shown that by leveraging the dynamical systems viewpoint of an optimization algorithm, accelerated convergence to a saddle point can be obtained. Instead of requiring the objective function to be strongly-convex--strongly-concave (as necessitated for accelerated convergence of several saddle-point algorithms), uniform fixed-time convergence is guaranteed for functions satisfying only the two-sided Polyak-{L}ojasiewicz (PL) inequality. A large number of practical problems, including the robust least squares estimation, are known to satisfy the two-sided PL inequality. The proposed method achieves arbitrarily fast convergence compared to any other state-of-the-art method with linear or even super-linear convergence, as also corroborated in numerical case studies." @default.
- W4288727913 created "2022-07-30" @default.
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- W4288727913 date "2022-07-26" @default.
- W4288727913 modified "2023-10-16" @default.
- W4288727913 title "Fixed-Time Convergence for a Class of Nonconvex-Nonconcave Min-Max Problems" @default.
- W4288727913 doi "https://doi.org/10.48550/arxiv.2207.12845" @default.
- W4288727913 hasPublicationYear "2022" @default.
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