Analytical linear inequality systems and optimization

In many interesting semi-infinite programming problems, all the constraints are linear inequalities whose coefficients are analytical functions of a o ne-dimensional parameter. This paper shows that significant geometrical inf ormation on the feasible set of these problems can be obtained directly fro m the given coefficient functions. One of these geometrical properties give s rise to a general purification scheme for linear semi-infinite programs e quipped with so-called analytical constraint systems. It is also shown that the solution sets of such kind of consistent systems form a transition cla ss between polyhedral convex sets and closed convex sets in the Euclidean s pace of the unknowns.