Different partitions of the parameter space of all linear semi-infinite programming problems with a fixed compact set of indices and continuous right and left hand side coefficients have been considered in this paper. The optimization problems are classified in a different manner, e.g., consistent and inconsistent, solvable (with bounded optimal value and nonempty optimal set), unsolvable (with bounded optimal value and empty optimal set) and unbounded (with infinite optimal value). The classification we propose generates a partition of the parameter space, called second general primal-dual partition. We characterize each cell of the partition by means of necessary and sufficient, and in some cases only necessary or sufficient conditions, assuring that the pair of problems (primal and dual), belongs to that cell. In addition, we show non emptiness of each cell of the partition and with plenty of examples we demonstrate that some of the conditions are only necessary or sufficient. Finally, we investigate various questions of stability of the presented partition.

A Monte Carlo simulation of the critical behaviour of a quite realistic FeBr2 model in a magnetic field has been performed. Two regions of different critical behaviour have been found in the temperature-field (T,H)-plane. At high temperature a region of continuous phase transitions is found with a crossover to a region of first-order (metamagnetic) phase transitions, in agreement with experimental results. Some of the main differences between FeBr2 and FeCl2 phase diagrams can also be reproduced.

Linear semi-infinite programming, linear systems, convex sets, 90C34, 15A39, 52A20,

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