On duality in semi-infinite programming and existence theorems for linear inequalities

Citation
Ma. Goberna et Ma. Lopez, On duality in semi-infinite programming and existence theorems for linear inequalities, J MATH ANAL, 230(1), 1999, pp. 173-192
Citations number
27
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
ISSN journal
0022247X → ACNP
Volume
230
Issue
1
Year of publication
1999
Pages
173 - 192
Database
ISI
SICI code
0022-247X(19990201)230:1<173:ODISPA>2.0.ZU;2-1
Abstract
Linear semi-infinite programming deals with the optimization of linear func tion als on finite-dimensional spaces under infinitely many linear constrai nts. For such kind of programs, a positive duality gap can occur between th em and their corresponding dual problems, which are linear programs posed o n infinite-dimensional spaces. This paper exploits some recent existence th eorems for systems of linear inequalities in order to obtain a complete cla ssification of linear semi-infinite programming problems from the point of view of the duality gap and the viability of the discretization numerical a pproach. The elimination of the duality gap is also discussed. (C) 1999 Aca demic Press.