Annals of Operations Research 101, 171–190, 2001  2001 Kluwer Academic Publishers. Manufactured in The Netherlands. Solving Strategies and Well-Posedness in Linear Semi-Infinite Programming ∗ M.J. CÁNOVAS canovas@umh.es Operations Research Center, Miguel Hernández University of Elche, E-03202 Elche (Alicante), Spain M.A. LÓPEZ ∗∗ marco.antonio@ua.es Department of Statistics and Operations Research, University of Alicante, E-03071 Alicante, Spain J. PARRA parra@umh.es Operations Research Center, Miguel Hernández University of Elche, E-03202 Elche (Alicante), Spain M.I. TODOROV mtodorov@fismat1.fcfm.buap.mx Benemérita Universidad Autónoma de Puebla, Facultad de Ciencias Físico-Matemáticas, Apdo. postal 1152, C.P. 72000 Puebla, Pue., Mexico Abstract. In this paper we introduce the concept of solving strategy for a linear semi-infinite programming problem, whose index set is arbitrary and whose coefficient functions have no special property at all. In particular, we consider two strategies which either approximately solve or exactly solve the approximating problems, respectively. Our principal aim is to establish a global framework to cope with different concepts of well-posedness spread out in the literature. Any concept of well-posedness should entail different proper- ties of these strategies, even in the case that we are not assuming the boundedness of the optimal set. In the paper we consider three desirable properties, leading to an exhaustive study of them in relation to both strate- gies. The more significant results are summarized in a table, which allows us to show the double goal of the paper. On the one hand, we characterize the main features of each strategy, in terms of certain stability prop- erties (lower and upper semicontinuity) of the feasible set mapping, optimal value function and optimal set mapping. On the other hand, and associated with some cells of the table, we recognize different notions of Hadamard well-posedness. We also provide an application to the analysis of the Hadamard well-posedness for a linear semi-infinite formulation of the Lagrangian dual of a nonlinear programming problem. Keywords: stability, Hadamard well-posedness, semi-infinite programming, feasible set mapping, optimal set mapping, optimal value function AMS subject classification: 90C34, 15A39, 49J53, 52A40 1. Introduction In this paper we present the concept of solving strategy in order to offer an unified treatment of different notions of Hadamard well-posedness for the linear optimization ∗ This research was partially supported by grants PB96-0335 and PB98-0975 from DGES and GV-C-CN- 10-067-96 from Generalitat Valenciana. ∗∗ Corresponding author.