  A numerical method is developed to solve linear semi-infinite programming
problem (LSIP) in which the iterates produced by the algorithm are feasible for
the original problem. This is achieved by constructing a sequence of standard
linear programming problems with respect to the successive discretization of
the index set such that the approximate regions are included in the original
feasible region. The convergence of the approximate solutions to the solution
of the original problem is proved and the associated optimal objective function
values of the approximate problems are monotonically decreasing and converge to
the optimal value of LSIP. An adaptive refinement procedure is designed to
discretize the index set and update the constraints for the approximate
problem. Numerical experiments demonstrate the performance of the proposed
algorithm.
