## Journals

- Advances in Mathematics of Communications
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### Open Access Journals

JIMO

In this paper, based on the ordering
relations induced by a pointed, closed and convex cone with a
nonempty interior, we propose a nonlinear augmented Lagrangian dual
scheme for a nonconvex multiobjective optimization problem by
applying a class of vector-valued nonlinear augmented Lagrangian
penalty functions. We establish the weak and strong duality results,
necessary and sufficient conditions for uniformly exact penalization
and exact penalization in the framework of nonlinear augmented
Lagrangian. Our results include several ones in the literature as
special cases.

JIMO

In this paper, the notion of generalized weak sharp minima is introduced for variational inequality problems
with functional constraints in finite-dimensional spaces by virtue of a dual gap function. Some equivalent and necessary conditions for
the solution set of the variational inequality problems to be a set of generalized weak sharp minima are obtained.

JIMO

Calculus rules of generalized $\epsilon-$subdifferential for
vector valued mappings and applications

In this paper, a generalized $\epsilon-$subdifferential, which was
defined by a norm, is first introduced for a vector valued mapping.
Some existence theorems and the properties of the generalized
$\epsilon-$subdifferential are discussed. A relationship between the
generalized $\epsilon-$subdifferential and a directional derivative
is investigated for a vector valued mapping. Then, the calculus
rules of the generalized $\epsilon-$subdifferential for the sum and
the difference of two vector valued mappings were given. The
positive homogeneity of the generalized $\epsilon-$subdifferential
is also provided. Finally, as applications, necessary and sufficient
optimality conditions are established for vector optimization
problems.

JIMO

This paper deals with the lower semicontinuity of the solution mapping to a parametric generalized
vector equilibrium problem. Under new assumptions, which do not contain any information about solution mappings,
we establish the lower semicontinuity of the solution mapping to a parametric generalized vector equilibrium
problem by using a scalarization method. These results improve the corresponding ones in recent literature.
Some examples are given to illustrate our results.

JIMO

In this paper, the lower semicontinuity of the approximate solution mapping to generalized strong vector equilibrium
problems is established by using a new proof method which is
different from the ones used in the literature. Simultaneously, we
also obtain the upper semicontinuity of the approximate solution mapping without the assumptions about monotonicity and
approximate solution mappings. Some examples are given to illustrate our results.

JIMO

In this paper, on one hand, we discuss upper Hölder type estimates of solutions to parametric vector quasi-equilibria with general settings, which generalize and extend the results of Chen et al. (Optim. Lett. 5: 85-98, 2011). On the other hand, combining the technique used for primal problems with suitable modifications, we also study upper Hölder type estimates of solutions to Minty-type parametric dual vector quasi-equilibria. The consequences obtained for dual problems are new in the literature.

NACO

This Special Issue of Numerical Algebra, Control and Optimization (NACO) is dedicated to Professor Franco Giannessi on the occasion of his 75th birthday and in recognition of his many fundamental contributions in Optimization and Nonlinear Analysis. It is a great honor and pleasure for the Guest Editors to have this opportunity to edit this Special Issue.

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NACO

In this paper, some properties are
established for second-order adjacent derivatives of set-valued maps. Upper and lower semicontinuity and
closedness are obtained for second-order adjacent derivatives of weak perturbation maps in vector optimization
problems. Several examples are given for illustrating our results.

NACO

In this paper, Robinson's metric regularity of a positive order around/at some point of parametric variational systems is discussed. Under some suitable conditions, the
relationships among H$\ddot{o}$lder-likeness, H$\ddot{o}$lder calmness, metric regularity of a positive order and Robinson's metric regularity of a positive order are discussed for the parametric variational systems. Then, some applications to the stabilities of the optimal value map and the solution map are studied for a parametric vector optimization problem, respectively.

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