150 research outputs found
A New Exceptional Family of Elements and Solvability of General Order Complementarity Problems
By using the concept of exceptional family, we propose
a sufficient condition of a solution to general order complementarity problems (denoted by GOCP) in Banach space, which is weaker than that in Németh, 2010 (Theorem 3.1). Then
we study some sufficient conditions for the nonexistence of exceptional family for
GOCP in Hilbert space. Moreover, we prove that without exceptional family is
a sufficient and necessary condition for the solvability of pseudomonotone general
order complementarity problems
Solvability of the G_2 Integrable System
It is shown that the 3-body trigonometric G_2 integrable system is
exactly-solvable. If the configuration space is parametrized by certain
symmetric functions of the coordinates then, for arbitrary values of the
coupling constants, the Hamiltonian can be expressed as a quadratic polynomial
in the generators of some Lie algebra of differential operators in a
finite-dimensional representation. Four infinite families of eigenstates,
represented by polynomials, and the corresponding eigenvalues are described
explicitly.Comment: 18 pages, LaTeX, some minor typos correcte
Lattice-like operations and isotone projection sets
By using some lattice-like operations which constitute extensions of ones
introduced by M. S. Gowda, R. Sznajder and J. Tao for self-dual cones, a new
perspective is gained on the subject of isotonicity of the metric projection
onto the closed convex sets. The results of this paper are wide range
generalizations of some results of the authors obtained for self-dual cones.
The aim of the subsequent investigations is to put into evidence some closed
convex sets for which the metric projection is isotonic with respect the order
relation which give rise to the above mentioned lattice-like operations. The
topic is related to variational inequalities where the isotonicity of the
metric projection is an important technical tool. For Euclidean sublattices
this approach was considered by G. Isac and respectively by H. Nishimura and E.
A. Ok.Comment: Proofs of Theorem 1 and Corollary 4 have been corrected. arXiv admin
note: substantial text overlap with arXiv:1210.232
Solving variational inequalities defined on a domain with infinitely many linear constraints
We study a variational inequality problem whose domain is defined by infinitely many linear inequalities. A discretization method and an analytic center based inexact cutting plane method are proposed. Under proper assumptions, the convergence results for both methods are given. We also provide numerical examples to illustrate the proposed method
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