Abstract
In the first part, different characterizations for the dimension of the feasible set in linear semi-infinite programming are provided. They involve the corresponding dimensions of some parameter sets, as the consequent inequalities cone and its lineality subspace. The remaining sections of the paper deal with Farkas–Minkowski systems. The third section is devoted to establish some results concerning the optimal set and its dimension, exploiting its strong relation with a particular parameter cone associated with the corresponding unstable constraints. The last section approaches the finite reducibility problem. We have intended to characterize those finite subproblems with the same optimal value as the original problem, by means of a simplc dual analysis, based on the main results derived before.
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