## Journals

- Advances in Mathematics of Communications
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- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
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JIMO

An alternating linearization method with inexact data, for the bilevel problem
of minimizing a nonsmooth convex function over the optimal solution set of another
nonsmooth convex problem, is presented in this paper. The problem is first approximately
transformed into an unconstrained optimization with the help of a penalty
function and we prove that the penalty function admits exact penalization under some mild conditions. The
objective function of this unconstrained problem is the sum of two nonsmooth convex
functions and in the algorithm each iteration involves solving two easily solved subproblems.
It is shown that the iterative sequence converges to a solution of the original problem by
parametric minimization theorem. Numerical experiments validate the theoretical convergence
analysis and illustrate the
implementation
of the alternating linearization algorithm
for this bilevel program.

JIMO

In this paper, we
consider using the inexact nonsmooth Newton method to efficiently
solve the symmetric cone constrained variational inequality (VISCC)
problem. It red provides a unified framework for dealing
with the variational inequality with nonlinear constraints,
variational inequality with the second-order cone constraints, and
the variational inequality with semidefinite cone constraints. We
get convergence of the above method
and apply the results to three special types symmetric cones.

DCDS-B

Using stochastic differential equations with Lévy jumps,
this paper studies the effect of environmental stochasticity and
random catastrophes on the permanence
of Lotka-Volterra facultative systems.
Under certain simple assumptions, we establish the sufficient conditions
for weak permanence in the mean
and extinction of the non-autonomous system, respectively.
In particular,
a necessary and sufficient condition for permanence
and extinction of autonomous system with jump-diffusion are obtained.
We generalize some former results under weaker assumptions.
Finally, we discuss the biological implications of the main
results.

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