Appl Math Optim 48:181–193 (2003)
2003 Springer-Verlag New York Inc.
A Generic Result in Linear Semi-Inﬁnite Optimization
Miguel A. Goberna,
Marco A. L´opez,
and Maxim I. Todorov
Department of Statistics and Operations Research,
Faculty of Sciences, Alicante University,
Ctra. San Vicente de Raspeig s/n, 03071 Alicante, Spain
Department of Physics and Mathematics, UDLA,
Cholula, Puebla, C.P. 72820, Mexico
Communicated by J. Stoer
Abstract. In this paper we consider the space of all the linear semi-inﬁnite pro-
gramming problems with the same index set, endowed with a suitable topology. We
provide a constructive proof of the following generic result: if we conﬁne ourselves
to the class of problems having a bounded set of coefﬁcient vectors (those vectors
appearing in the left-hand side of the constraints), the set of those problems which
have a strongly unique optimal solution contains an open and dense subset of the
set of solvable problems in the same class.
Key Words. Semi-inﬁnite linear optimization, Strong unique solution, Stability
AMS Classiﬁcation. Primary 90C34, 90C05, Secondary 90C25, 52A20.
We consider linear optimization problems, in R
, of the form
x | a
x ≥ b
, t ∈ T },
The third author is on leave from IMI-BAS, Soﬁa, Bulgaria. This work has been supported by MCYT
of Spain and FEDER of EU, Grant BMF2002-04114-C02-01.