Solving convex programs with infinitely many linear constraints by a relaxed cutting plane method

One of the major computational bottlenecks of using the conventional cutting plane approach to solve convex programming problems with infinitely many linear constraints lies in finding a global optimizer of a nonlinear and nonconvex program. This paper presents a relaxed scheme to generate a new cut. In each iteration, the proposed scheme chooses a point at which the constraints are violated to a degree rather than at which the violation is maximized. A convergence proof is provided. The proposed scheme also exhibits the capability of generating an approximate solution to any level of accuracy in a finite number of iterations.