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- W2138601654 abstract "Due to its simplicity and numerical efficiency for unconstrained optimization problems, the spectral gradient method has received more and more attention in recent years. In this paper, two spectral gradient projection methods for constrained equations are proposed, which are combinations of the well-known spectral gradient method and the hyperplane projection method. The new methods are not only derivative-free, but also completely matrix-free, and consequently they can be applied to solve large-scale constrained equations. Under the condition that the underlying mapping of the constrained equations is Lipschitz continuous or strongly monotone, we establish the global convergence of the new methods. Compared with the existing gradient methods for solving such problems, the new methods possess a linear convergence rate under some error bound conditions. Furthermore, a relax factor γ is attached in the update step to accelerate convergence. Preliminary numerical results show that they are efficient and promising in practice." @default.
- W2138601654 created "2016-06-24" @default.
- W2138601654 creator A5040116817 @default.
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- W2138601654 date "2015-01-10" @default.
- W2138601654 modified "2023-09-27" @default.
- W2138601654 title "Two spectral gradient projection methods for constrained equations and their linear convergence rate" @default.
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- W2138601654 doi "https://doi.org/10.1186/s13660-014-0525-z" @default.
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