## Journals

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### Open Access Journals

KRM

We consider the diffusive limit of an unsteady neutron transportequation in a two-dimensional plate with one-speed velocity. We show the solution can be approximated by the sum of interior solution, initial layer, and boundary layer with geometric correction. Also, we construct a counterexample to the classical theory in [

IPI

In this paper, we propose an iterative method for solving the $\ell_1$-regularized minimization
problem $\min_{x\in\mathbb{R}^n} f(x)+\rho^T |x|$, which has great applications in the areas of
compressive sensing. The construction of our method consists of two main steps:
(1) to reformulate an $\ell_1$-problem into a nonsmooth equation $h^\tau(x)={\bf 0}$, where ${\bf 0}\in \mathbb{R}^n$ is the zero vector; and
(2) to use $-h^\tau(x)$ as a search direction. The proposed method can be regarded as
spectral residual method because we use the residual as a search direction at each iteration.
Under mild conditions, we establish the global convergence of the method
with a nonmonotone line search. Some numerical
experiments are performed to compare the behavior of the proposed method with three
other methods. The results positively support the proposed method.

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