A Cutting-Plane Method with Updating of Approximating Sets and Estimates of the Solution Accuracy

We propose a cutting-plane method for solving a mathematical programming problem. A sequence of approximations is constructed using the technique of partial immersion of the admissible set in the approximating polyhedral sets. The developed method does not require the inclusion of each of the approximating sets in the previous one. This peculiarity makes it possible to periodically drop any additional planes which occur in the problem-solving process. We describe the features of the method, prove its convergence, and obtain estimates of the solution accuracy.