Showing papers on "Isotone published in 1995"
01 Jan 1995
TL;DR: Dykstra's cyclic projections algorithm, as well as what is known about its rate-of-convergence, are described in this article, where its applications to isotone and convex regression, and linear and quadratic programming are mentioned.
Abstract: Dykstra’s cyclic projections algorithm, as well as what is known about its rate-of-convergence, are described. Its applications to isotone and convex regression, and linear and quadratic programming are mentioned.
11 citations
TL;DR: It is shown that for cycle-free ordered sets, the ratio | Aut ( P )|/| End ( P)| converges to zero as |P| goes to infinity.
7 citations
TL;DR: A necessary and sufficient condition for a differentiable transformation to be isotone w.r.t. cone preorderings on a convex set is given in this article, which is applied to characterize monotone matrix functions A ↦ A p with integer p ≥ 2.
5 citations
TL;DR: A class of objective functions and a class of polyhedral feasible sets which provide the optimal greedy solution for the problem max{f(x)/vbx ϵ D ⊂ R n } .
5 citations
TL;DR: In this paper, it was shown that for a distributive lattice, all unary functions with the Substitution Property are ID-polynomials if and only ifL contains no proper Boolean interval.
Abstract: A universal algebra isaffine complete if all functions satisfying the Substitution Property are polynomials (composed of the basic operations and the elements of the algebra). In 1962, the first author proved that a bounded distributive lattice is affine complete if and only if it does not contain a proper Boolean interval. Recently, M. Ploscica generalized this result to arbitrary distributive lattices. In this paper, we introduce a class of functions on a latticeL, we call themID-polynomials, that derive from polynomials on the ideal lattice (resp., dual ideal lattice) ofL; they are isotone functions and satisfy the Substitution Property. We prove that for a distributive latticeL, all unary functions with the Substitution Property are ID-polynomials if and only ifL contains no proper Boolean interval.
4 citations