We state second order necessary optimality conditions for a vector optimization problem with an arbitrary feasible set and an order in the final space given by a pointed convex cone with nonempty interior. We establish, in finite-dimensional spaces, second order optimality conditions in dual...

The purpose of this paper is to investigate differential properties of a class of set-valued maps and gap functions involving vector variational inequalities. Relationship between their contingent derivatives are discussed. A formula computing contingent derivative of the gap functions is...

This work deals with strategy optimization for electricity producers. We consider two types of auctions used to maintain the real-time ballance for production and consumption of electricity. For both auction types, we calculate the market equilibrium and discuss its properties. Copyright...

We study a notion of well-posedness in vector optimization through the behaviour of minimizing sequences of sets, defined in terms of Hausdorff set-convergence. We show that the notion of strict efficiency is related to the notion of well-posedness. Using the obtained results we identify a class...

A discrete mass transportation problem, studied by Kellerer, is extended to the case of infinitely many sites. An application to general representant systems is given, which generalizes M. Hall's extension of P. Hall's theorem to the case of infinite families of sets. Copyright Springer-Verlag 2003

In this paper, a new trust region method for the system of nonlinear equations is presented in which the determining of the trust region radius incorporates the information of its natural residual. The global convergence is obtained under mild conditions. Unlike traditional trust region method,...

We introduce a family of undiscounted branching bandits on parallel servers under controls which can impose priorities between customer classes. This family can be used to model a wide range of multi-class queueing scheduling problems, with the capacity to incorporate problem features such as...

We consider the Poisson equations for denumerable Markov chains with unbounded cost functions. Solutions to the Poisson equations exist in the Banach space of bounded real-valued functions with respect to a weighted supremum norm such that the Markov chain is geometrically ergodic. Under minor...

This paper considers the problem of searching for good second-order multiple recursive generators (MRGs) with long period and good lattice structure. An adaptive genetic algorithm with reversals is proposed. The proposed algorithm is compared with forward/backward and random methods, and its...

In this paper, the feasible type SQP method is improved. A new algorithm is proposed to solve nonlinear inequality constrained problem, in which a new modified method is presented to decrease the computational complexity. It is required to solve only one QP subproblem with only a subset of the...