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
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.