One approach to constructing cutting algorithms with dropping of cutting planes

We propose a general cutting method for conditional minimization of continuous functions. We calculate iteration points by partially immersing the admissible set in approximating polyhedral sets. We describe the features of the proposed method and prove its convergence. The constructed general method does not imply the inclusion of each of approximating sets in the previous one. This feature allows us to construct cutting algorithms which periodically drop any additional restrictions which occur in the solution process.