A ladder method for linear semi-infinite programming

This paper presents a new method for linear semi-infinite pro- gramming. With the introduction of the so-called generalized ladder point, a ladder method for linear semi-infinite programming is developed. This work includes the generalization of the inclusive cone version of the fundamental theorem of linear programming and the extension of a linear programming lad- der algorithm. The extended ladder algorithm finds a generalized ladder point optimal solution of the linear semi-infinite programming problem, which is ap- proximated by a sequence of ladder points. Simple convergence properties are provided. The algorithm is tested by solving a number of linear semi-infinite programming examples. These numerical results indicate that the algorithm is very efficient when compared with other methods.