Solutions of a variational inequality problem defined by a closed and convex set and a
mapping are found by imposing conditions for the monotone convergence with respect to a …

In this paper, we study a new generalization of the Lorentz cone L^ n_+ L+ n, called the
monotone extended second-order cone (MESOC). We investigate basic properties of …

Error bounds are a requisite for trusting or distrusting solutions in an informed way. Until
recently, provable error bounds in the absence of constraint qualifications were unattainable …

The extended second order cones were introduced by Németh and Zhang (J Optim Theory
Appl 168 (3): 756–768, 2016) for solving mixed complementarity problems and variational …

In this paper, we first discuss the geometric properties of the Lorentz cone and the extended
Lorentz cone. The self-duality and orthogonality of the Lorentz cone are obtained in Hilbert …

In this paper, we investigate the structure of Lyapunov-like transformations on the extended
second order cone, considered as a multivariate version of topheavy cone with respect to an …

This paper explores the nonconvex second-order cone as a nonconvex conic extension of
the known convex second-order cone in optimization, as well as a higher-dimensional conic …

In this paper, we study the linear complementarity problems on extended second order
cones. We convert a linear complementarity problem on an extended second order cone …

We study and solve the two-stage stochastic extended second-order cone programming
problem. We show that the barrier recourse functions and the composite barrier functions for …

In this paper, as an extension of the isotone projection cone, we consider the isotonicity of
the metric projection operator with respect to the mutually dual orders induced by the cone …