7 citations · 14 across the 9 of their papers we have counts for
10 papers
Face relative interior of convex sets in topological vector spaces
Reinier Díaz Mill án, Vera Roshchina
A new notion of face relative interior for convex sets in topological real vector spaces is introduced in this work. Face relative interior is grounded in the facial structure, and…
Application and issues in abstract convexity
Reinier Díaz Millán, Nadezda Sukhorukova, Julien Ugon
The theory of abstract convexity, also known as convexity without linearity, is an extension of the classical convex analysis. There are a number of remarkable results, mostly conc…
The intrinsic core and minimal faces of convex sets in general vector spaces
R. Díaz Millán, Vera Roshchina
Intrinsic core generalises the finite-dimensional notion of the relative interior to arbitrary (real) vector spaces. Our main goal is to provide a self-contained overview of the ke…
Multivariate approximation by polynomial and generalised rational functions
R. Díaz Millán, V. Peiris, N. Sukhorukova +1
In this paper we develop an optimisation based approach to multivariate Chebyshev approximation on a finite grid. We consider two models: multivariate polynomial approximation and…
An algorithm for best generalised rational approximation of continuous functions
R. Díaz Millán, Nadezda Sukhorukova, Julien Ugon
The motivation of this paper is the development of an optimisation method for solving optimisation problems appearing in Chebyshev rational and generalised rational approximation p…
Inexact proximal -subgradient methods for composite convex optimization problems
Reinier Díaz Millán, Majela Pentón Machado
We present two approximate versions of the proximal subgradient method for minimizing the sum of two convex functions (not necessarily differentiable). The algorithms involve, at e…