## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- 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
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- AIMS Mathematics
- Conference Publications
- Electronic Research Announcements
- Mathematics in Engineering

### Open Access Journals

JIMO

We present a class of gap functions for the quasi-variational
inequality problem (QVIP). We show the equivalence between the optimization
reformulation with the gap function and the original QVIP.
We also give conditions under which the gap function is continuous
and directionally differentiable.

JIMO

We consider a class of stochastic
mathematical programs with equilibrium constraints (SMPECs), in
which all decisions are required to be made here-and-now, before a
random event is observed. We show that this kind of SMPEC plays a
very important role in practice. In order to develop effective
algorithms, we first give some reformulations of the SMPEC and
then, based on these reformulations, we propose a smoothed penalty
approach for solving the problem. A comprehensive convergence
theory is also included.

JIMO

In this paper, a portfolio selection model with a combined
Worst-Case Conditional Value-at-Risk (WCVaR) and Multi-Factor Model is proposed.
It is shown that the probability distributions in the definition of WCVaR can be determined by specifying
the mean vectors under the assumption of multivariate normal distribution
with a fixed variance-covariance matrix. The WCVaR minimization problem is then
reformulated as a linear programming problem. In our numerical experiments,
to compare the proposed model with the traditional mean variance model,
we solve the two models using the real market data and present
the efficient frontiers to illustrate the difference. The comparison reveals
that the WCVaR minimization model is more robust than the traditional
one in a market recession period and it can be used in a long-term
investment.

NACO

Evolutionary Algorithms (EAs) provide a very powerful tool for
solving optimization problems. In the last decades, numerous
studies have been focusing on improving the performance of EAs.
However, there is a lack of studies that tackle the question of
the termination criteria. Indeed, EAs still need termination
criteria prespecified by the user. In this paper, we propose to
combine the Differential Evolution (DE) method with novel
elements, i.e., the ``Gene Matrix'' (GM), the ``Space
Decomposition'' (SD) and ``Space Rotation'' (SR) mechanisms, in
order to equip DE with an automatic termination criterion without
resort to predefined conditions. We name this algorithm
``Differential Evolution with Automatic Termination'' (DEAT).
Numerical experiments using a test bed of widely used benchmark
functions in 10, 50 and 100 dimensions show the effectiveness of
the proposed method.

JIMO

We propose an iterative method that solves a nonsmooth
convex optimization problem by converting the original
objective function to a once continuously differentiable
function by way of Moreau-Yosida regularization.
The proposed method makes use of approximate function
and gradient values of the Moreau-Yosida regularization
instead of the corresponding exact values.
Under this setting, Fukushima and Qi (1996) and Rauf
and Fukushima (2000) proposed a proximal Newton method and
a proximal BFGS method, respectively, for nonsmooth convex optimization.
While these methods employ a line search strategy
to achieve global convergence, the method proposed in this paper
uses a trust region strategy.
We establish global and superlinear convergence of the method
under appropriate assumptions.

JIMO

Road pricing is considered one of the effective
means to reduce traffic congestion and environmental damage, and it
has been introduced in major highways
of most countries. The road pricing problem can be formulated as a
mathematical program with equilibrium constraints (MPEC) and the
resulting MPEC can be solved efficiently by the implicit programming
approach if the user's route costs are additive. However, route
costs are generally nonadditive in the real world. In this paper we
consider road pricing on the traffic equilibrium problem
with nonadditive route costs based on users' disutility functions. We then show that this formulation
can be reformulated as a mathematical program with strictly monotone
mixed complementarity problem (MCP). Since a strictly monotone MCP
has a unique solution for each upper level variable, we can apply the implicit programming
approach to solve the resulting reformulation. We establish the differentiability of the
resulting implicit function.
Numerical experiments using various disutility functions and sample networks are done, and the
results show that the implicit programming approach is robust to find a
solution of the road pricing problem.

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