Relaxed Cutting Plane Method for Solving Linear Semi-innnite Programming Problems

One of the major computational tasks of using the traditional cutting plane approach to solve linear semi-in nite programming problems lies in nding a global optimizer of a non-linear and non-convex program. This paper generalizes Gustafson and Kortanek's scheme to relax this requirement. In each iteration, the proposed method chooses a point at which the in nite constraints are violated to a degree rather than at which the violation are maximized. A convergence proof of the proposed scheme is provided. Some computational results are included. An explicit algorithm which allows the unnecessary constraints to be dropped in each iteration is also introduced to reduce the size of computed programs.