Solving strategies and well-posedness in linear semi-infinite programming

In this paper we introduce the concept of solving strategy for a linear sem i-infinite programming problem, whose index set is arbitrary and whose coef ficient functions have no special property at all. In particular, we consid er two strategies which either approximately solve or exactly solve the app roximating problems, respectively. Our principal aim is to establish a glob al framework to cope with different concepts of well-posedness spread out i n the literature. Any concept of well-posedness should entail different pro perties 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 pr operties, 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 t he main features of each strategy, in terms of certain stability properties (lower and upper semicontinuity) of the feasible set mapping, optimal valu e function and optimal set mapping. On the other hand, and associated with some cells of the table, we recognize different notions of Hadamard well-po sedness. We also provide an application to the analysis of the Hadamard wel l-posedness for a linear semi-infinite formulation of the Lagrangian dual o f a nonlinear programming problem.