On the convergence of cutting plane algorithms for a class of nonconvex mathematical programs

We discuss the convergence of cutting plane algorithms for a class of nonconvex programs called the Generalized Lattice Point Problems (GLPP). A set of sufficient conditions which guarantee finite convergence are presented. Although these conditions are usually difficult to enforce in a practical implementation, they do illustrate the various factors that must be involved in a convergent rudimentary cutting plane algorithm. A striking example of nonconvergence (in which no subsequence converges to a feasible solution, even when seemingly strong cutting planes are used), is presented to show the effect of neglecting one such factor. We give an application of our analysis to problems with multiple choice constraints and finally discuss a modification of cutting plane algorithms so as to make finite convergence more readily implementable.