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- W3163342783 abstract "• A rank-one modification is performed on the classical BFGS update for the Hessian. • The given updating formula satisfies an extended secant equation. • An augmented version of the BFGS method is developed. • The method can be efficiently used to solve practical large-scale optimization problems. Making a rank-one modification on the classical BFGS (Broyden–Fletcher–Goldfarb–Shanno) updating formula, we develop a class of augmented BFGS methods. The suggested formula can be considered as a hybridization of the basic BFGS updating formula for Hessian with an additional rank-one term embedded to guarantee a general modified secant equation. By using the well-known Sherman–Morrison formula, the inverse of a memoryless version of the given updating formula is computed to be applied for solving large-scale problems. Convergence analysis is concisely carried out as well. At last, the practical merits of the method are investigated by numerical tests on a set of CUTEr problems as well as the well-known compressed sensing problem. Results show the computational efficiency of the given method." @default.
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- W3163342783 date "2021-09-01" @default.
- W3163342783 modified "2023-09-24" @default.
- W3163342783 title "An augmented memoryless BFGS method based on a modified secant equation with application to compressed sensing" @default.
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- W3163342783 doi "https://doi.org/10.1016/j.apnum.2021.05.002" @default.
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