Local polynomial functions on semilattices

Quasi-concave functions on meet-semilattices

This paper deals with maximization of set f'unctions delined as minimum values of monotone linkage functions. In previous research, it has been shown that such a set function can be maximized by a greedy type algorithm over a family of all subsets of a finite set. ln this paper, we extend this finding to meet-semilattices. We show that the class of functions defined as minimum values of monoton...

Local Minimax Learning of Approximately Polynomial Functions

Suppose we have a number of noisy measurements of an unknown real-valued function f near a point of interest x0 ∈ R. Suppose also that nothing can be assumed about the noise distribution, except for zero mean and bounded covariance matrix. We want to estimate f at x0 using a general linear parametric family f(x; a) = a0h0(x) + . . . + aqhq(x), where a ∈ R and hi’s are bounded functions on a nei...

Local Self-concordance of Barrier Functions Based on Kernel-functions

 Many efficient interior-point methods (IPMs) are based on the use of a self-concordant barrier function for the domain of the problem that has to be solved. Recently, a wide class of new barrier functions has been introduced in which the functions are not self-concordant, but despite this fact give rise to efficient IPMs. Here, we introduce the notion of locally self-concordant barrier functio...

Polynomial Functions on Bounded Chains

We are interested in representations and characterizations of lattice polynomial functions f : L → L, where L is a given bounded distributive lattice. In an earlier paper [4, 5], we investigated certain representations and provided various characterizations of these functions both as solutions of certain functional equations and in terms of necessary and sufficient conditions. In the present pa...

Hermite Interpolation Using ERBS with Trigonometric Polynomial Local Functions