Selected Applications of Linear Semi-Infinite Systems Theory

被引：7

作者：

Goberna, Miguel A. ^{[1
]}

Ridolfi, Andrea B. ^{[2
,3
]}

Vera de Serio, Virginia N. ^{[3
]}

机构：

[1] Univ Alicante, Dept Math, Alicante, Spain

[2] Univ Nacl Cuyo, Fac Ciencias Aplicadas Ind, Mendoza, Argentina

[3] Univ Nacl Cuyo, Fac Ciencias Econ, Mendoza, Argentina

来源：

VIETNAM JOURNAL OF MATHEMATICS | 2020年 / 48卷 / 03期

关键词：

Linear inequality systems; Computational geometry; Voronoi cells; epsilon-subdifferentials; SEMI-INFINITE PROGRAMS; FEASIBLE SET; INEQUALITY SYSTEMS; ILL-POSEDNESS; UPPER SEMICONTINUITY; STABILITY THEORY; ROBUST SOLUTIONS; OPTIMIZATION; DUALITY; REPRESENTATIONS;

D O I：

10.1007/s10013-020-00415-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we, firstly, review the main known results on systems of an arbitrary (possibly infinite) number of weak linear inequalities posed in the Euclidean space Rn (i.e., with n unknowns), and, secondly, show the potential power of this theoretical tool by developing in detail two significant applications, one to computational geometry: the Voronoi cells, and the other to mathematical analysis: approximate subdifferentials, recovering known results in both fields and proving new ones. In particular, this paper completes the existing theory of farthest Voronoi cells of infinite sets of sites by appealing to well-known results on linear semi-infinite systems.

引用

页码：439 / 470

页数：32

共 70 条

[1] AN EXTENSION OF THE SIMPLEX ALGORITHM FOR SEMI-INFINITE LINEAR-PROGRAMMING [J].