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This implicit hybrid method with regularization is based on the CQ method, extragradient method and gradient projection algorithm with regularization.
The multi-step implicit iterative method with regularization is based on three well-known methods: the extragradient method, approximate proximal method and gradient projection algorithm with regularization.
Another is an implicit hybrid method with regularization which is based on the CQ method, extragradient method and gradient projection algorithm with regularization.
On the other hand, we also establish a strong convergence result via an implicit hybrid method with regularization for solving these two problems.
This implicit iterative method with regularization is based on the extragradient method, approximate proximal method and gradient projection algorithm (GPA) with regularization.
This implicit hybrid method with regularization is based on the CQ method, extragradient method and gradient projection algorithm (GPA) with regularization.
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The iterative algorithm is based on Korpelevich's extragradient method, viscosity approximation method, Mann's iteration method, hybrid steepest-descent method and gradient-projection method (GPM) with regularization.
Some authors used methods with regularization to solve the minimization problems (see [6]), and the other methods for hierarchical minimization problems (see [7]).
Traditionally nonlinear inverse problems in discrete form have been solved via local optimization methods with regularization, but linear analysis techniques failed to account for the uncertainty in the solution that it is adopted.
Motivated and inspired by the above facts, we introduce and analyze a multistep hybrid extragradient algorithm by combining Korpelevich's extragradient method, the viscosity approximation method, thehybrid steepest-descent method, Mann's iteration method, and the gradient-projection method (GPM) with regularization in the setting of infinite-dimensional Hilbert spaces.
By combining Korpelevich's extragradient method, the viscosity approximation method, the hybrid steepest-descent method, Mann's iteration method, and the gradient-projection method (GPM) with regularization, we introduce and analyze a hybrid multi-step extragradient algorithm with regularization in the setting of Hilbert spaces.
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Justyna Jupowicz-Kozak
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