Time integration methods for solving initial value problems are an important component of many scientific and engineering simulations. Implicit time integrators desirable their stability properties, significantly relaxing restrictions on timestep size. However, implicit require solutions to one or more systems nonlinear equations at each timestep, which large simulations can be prohibitively ex...

A regularized minimization model with $l_1$-norm penalty (RP) is introduced for training the autoencoders that belong to a class of two-layer neural networks. We show RP can act as an exact which shares same global minimizers, local and d(irectional)-stationary points original under mild conditions. construct bounded box region contains at least one minimizer RP, propose linearly constrained (L...